Set Theory Talks

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

CMU events starting next week

Carnegie Mellon Logic Seminar

1/29/2021 21:30:55

TUESDAY, February 2, 2021 Mathematical logic seminar: 3:30 P.M., Online, Anush Tserunyan, McGill University Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Ergodic theorems along trees ABSTRACT: In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation $T$, one takes averages of a given integrable function over the intervals $\{x, T(x), T^2(x), \hdots, T^n(x)\}$ in front of the point $x$. We prove a “backward” ergodic theorem for a countable-to-one pmp $T$, where the averages are taken over subtrees of the graph of T that are rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$). Surprisingly, this theorem yields forward ergodic theorems for countable groups, in particular, one for pmp actions of free groups of finite rank, where the averages are taken along subtrees of the standard Cayley graph rooted at the identity. This strengthens Bufetov’s theorem from 2000, which was the most general result in this vein. This is joint work with Jenna Zomback. TUESDAY, February 2, 2021 Set Theory Reading Group: 4:30 P.M., Online, Jenna Zomback, University of Illinois at Urbana-Champaign Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Ergodic theorems along trees: the proofs ABSTRACT: In this continuation of the previous talk, we discuss a backward (inverse) ergodic theorem for a probability measure preserving (pmp) transformation $T$, where the averages are taken over subtrees of the graph of $T$ that are rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$). We will derive from it a new (forward) pointwise ergodic theorem for pmp actions of free groups of finite rank, where the averages are taken along subtrees of the standard Cayley graph rooted at the identity. We will then discuss a very short proof (due to Tserunyan) of the classical pointwise ergodic theorem, and, using this proof as an outline, we will sketch the proof of the backward ergodic theorem. This is joint work with Anush Tserunyan. THURSDAY, February 4, 2021 Model Theory Seminar: 10:00 A.M., Online, John Baldwin, UIC Join Zoom Meeting: https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09 Meeting ID: 963 0186 9290 Passcode: 567655 TITLE: The Hanf number for extendability is the first measurable cardinal, Part 1 ABSTRACT: We prove in ZFC the existence of a complete sentence of infinitary logic that has maximal models in a set of cardinals cofinal in the first measurable but no maximal models in any cardinal beyond the first measurable. As a warmup to the first lecture please look at the Motivation http://homepages.math.uic.edu/~jbaldwin/pub/cmupre This is joint work with Saharon Shelah. Preprints are available at http://homepages.math.uic.edu/~jbaldwin/pub/ahanfmaxjan21.pdf and http://homepages.math.uic.edu/~jbaldwin/pub/ahazfjan7.pdf TUESDAY, February 9, 2021 Mathematical logic seminar: 3:30 P.M., Online, Benjamin Siskind, University of California, Berkeley Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Order-preserving Martin’s Conjecture ABSTRACT: Martin’s Conjecture is a precise way of asserting that, up to equivalence, the only natural functions on the Turing degrees are the familiar ones: the constant functions, the identity, the Turing jump, and the transfinite iterates of the Turing jump. This conjecture is open even restricted to low-level Borel functions, but there have been partial results over the years which show it holds for classes of functions meeting requirements orthogonal to definability. Our recent result is that part of Martin’s Conjecture (lately called “part one”) holds for the class of order-preserving functions. In particular, it follows that the full Martin’s Conjecture holds for Borel order-preserving functions. We’ll talk about Martin’s Conjecture broadly and say something about this recent work. This is joint work with Patrick Lutz. TUESDAY, February 9, 2021 Set Theory Reading Group: 4:30 P.M., Online, Benjamin Siskind, University of California, Berkeley Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Measure-preserving functions on the Turing degrees ABSTRACT: One proof of part one of Martin’s Conjecture for order-preserving functions works for a bigger class of functions: those which are measure-preserving for the Martin measure, in the sense of ergodic theory. Looking at this class of functions brings out more set-theoretic aspects of Martin’s Conjecture. For example, part one of Martin’s Conjecture is equivalent to the non-existence of other non-principal ultrafilters on the Turing degrees Rudin-Keisler below the Martin measure. We’ll talk about the proof of part one of Martin’s Conjecture for this class of functions and some consequences. This is joint work with Patrick Lutz. THURSDAY, February 11, 2021 Model Theory Seminar: 10:00 A.M., Online, John Baldwin, UIC Join Zoom Meeting: https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09 Meeting ID: 963 0186 9290 Passcode: 567655 TITLE: The Hanf number for extendability is the first measurable cardinal, Part 2 ABSTRACT: We prove in ZFC the existence of a complete sentence of infinitary logic that has maximal models in a set of cardinals cofinal in the first measurable but no maximal models in any cardinal beyond the first measurable. As a warmup to the first lecture please look at the Motivation http://homepages.math.uic.edu/~jbaldwin/pub/cmupre This is joint work with Saharon Shelah. Preprints are available at http://homepages.math.uic.edu/~jbaldwin/pub/ahanfmaxjan21.pdf and http://homepages.math.uic.edu/~jbaldwin/pub/ahazfjan7.pdf TUESDAY, February 16, 2021 Mathematical logic seminar: 3:30 P.M., Online, Aristotelis Panagiotopoulos, University of Muenster Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: The definable content of (co)homological invariants: Cech cohomology ABSTRACT: In this talk we will develop a framework for enriching various classical invariants of homological algebra and algebraic topology with additional descriptive set-theoretic information. The resulting "definable invariants" can be used for much finer classification than their purely algebraic counterparts. We will then illustrate how these ideas apply to the classical Cech cohomology theory, by introducing a new invariant for locally compact metrizable spaces up to homotopy equivalence which we call "definable cohomology". In strong contrast to its classical counterpart, this definable cohomology theory provides complete classification to homotopy classes of mapping telescopes of d-tori, and for homotopy classes of maps from mapping telescopes of d-tori to spheres. The latter problem was raised in the d=1 case by Borsuk and Eilenberg in 1936. This is joint work with Jeffrey Bergfalk and Martino Lupini. TUESDAY, February 16, 2021 Set Theory Reading Group: 4:30 P.M., Online, Aristotelis Panagiotopoulos, University of Muenster Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Ulam stability for quotients of abelian non-archimedean Polish groups ABSTRACT: Based on an earlier work of Shelah concerning the relationship of the continuum hypothesis to the cardinality of the set of automorphisms of $\mathcal{P}(\omega)/\mathrm{fin}$, Velickovic showed that if such an automorphism admits a Borel lift $\mathcal{P}(\omega)\to \mathcal{P}(\omega)$, then it is of a certain "trivial" form. Similarly, Kanovei and Reeken showed that if $N,M$ are countable dense subgroups of $\mathbb{R}$, then every homomorphism $\mathbb{R}/N\to \mathbb{R}/M$ with a Borel lift $\mathbb{R}\to \mathbb{R}$, is of a certain "trivial" form. Kanovei and Reeken asked whether quotients of the $p$-adic groups satisfy similar "Ulam stability" phenomena. In this talk, we will settle this question by providing Ulam-stability phenomena for definable homomorphisms $G/N\to H/M$ when $G,H$ are arbitrary abelian non-archimedean Polish groups and $N,M$ are Polishable subgroups. We will then illustrate how such rigidity results are in the heart of the definable cohomology theory which we developed in the previous talk. This is joint work with Jeffrey Bergfalk and Martino Lupini. TUESDAY, March 2, 2021 Mathematical logic seminar: 3:30 P.M., Online, Marc Noy, Technical University of Catalonia Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Zero-One and Convergence Laws for Graphs Embeddable on a Fixed Surface ABSTRACT: Let G be a class of labeled graphs with the uniform probability distribution on graphs with a fixed number of vertices. Given a graph property A, we are interested in the limiting probability that A holds in G. It was shown by Heinig et al. that this limiting probability always exists when G is the class of planar graphs and A is any property expressible in monadic second order logic (MSO), and it was conjectured that the same result holds for the class of graphs embeddable on a fixed surface S. After reviewing the results for planar graphs, and more generally for minor-closed classes of graphs, we will refute the conjecture by showing that for every closed surface (orientable or not) other than the sphere there exists an MSO graph property whose limiting probability does not exist. In addition we show that every rational number in [0,1] is the limiting probability of some MSO property, as opposed to the class of planar graphs where there are so-called gaps. The proof relies on a combination of methods from structural graph theory, concretely large face-width embeddings of graphs on surfaces, analytic combinatorics, and finite model theory. This is joint work with Albert Atserias and Stephan Kreutzer. TUESDAY, April 20, 2021 Mathematical logic seminar: 3:30 P.M., Online, Sandra Müller, University of Vienna Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: TBA TUESDAY, April 20, 2021 Set Theory Reading Group: 4:30 P.M., Online, Sandra Müller, University of Vienna Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: TBA

Tomorrow: Corey Switzer at 1 30 pm (Toronto Time)

Toronto Set Theory Seminar

1/28/2021 13:01:00

Hello everyone,

Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.

Here the speaker information:

Speaker: Corey Switzer, The Graduate Center, CUNY

Date and Time: Friday, January 29, 2021 - 1:30pm to 3:00pm (Toronto time)

Title: Higher Dimensional Cardinal Characteristics for Sets of Real Valued Functions

Abstract:

Cardinal characteristics on the generalized Baire and Cantor spaces $\kappa^\kappa$ and $2^\kappa$ have recently generated significant interest. In this talk I will introduce a different generalization of cardinal characteristics, namely to the space of functions $f:\omega^\omega \to \omega^\omega$. Given an ideal $I$ on Baire space and a relation $R$ let us define $f R_I g$ for $f$ and $g$ functions from $\omega^\omega$ to $\omega^\omega$ if and only if $f(x) R g(x)$ for an $I$-measure one set of $x \in \omega^\omega$. By letting $I$ vary over the null ideal, the meager ideal and the bounded ideal; and $R$ vary over the relations $\leq^*$, $\neq^*$ and $\in^*$ we get 18 new cardinal characteristics by considering the bounding and dominating numbers for these relations. These new cardinals form a diagram of provable implications similar to the Cichoń diagram. They also interact in several surprising ways with the cardinal characteristics on $\omega$. For instance, they can be arbitrarily large in models of CH, yet they can be $\aleph_1$ in models where the continuum is arbitrarily large. They are bigger in the Sacks model than the Cohen model. I will introduce these cardinals, show some of the provable implications and discuss what is known about consistent inequalities, focusing on the $\mathfrak{b}$-numbers in well-known models such as the Cohen and Random model. This is joint work with Jörg Brendle.

Bio: Corey Bacal Switzer is currently a postdoctoral researcher at the Kurt Gödel Research Center For Mathematical Logic in the Mathematics Department of the University of Vienna working under Vera Fischer. He finished his PhD at the CUNY Graduate Center in New York in 2020. His research is in set theory, focusing on forcing, cardinal characteristics and infinite combinatorics

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Logic Seminar 3 Feb 2021 17:00 hrs at NUS by Wong Tin Lok

NUS Logic Seminar

1/28/2021 3:41:46

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 3 February 2021, 17:00 hrs Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Speaker: Wong Tin Lok Title: Arithmetic under negated induction URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: Arithmetic generally does not admit any non-trivial quantifier elimination. I will talk about one exception, where the negation of an induction axiom is included in the theory. Here the Weak Koenig's Lemma from reverse mathematics arises as a model completion. This work is joint with Marta Fiori-Carones, Leszek Aleksander Kolodziejczyk and Keita Yokoyama.

Barcelona Set theory Seminar

Barcelona Logic Seminar

1/25/2021 11:50:42

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

SPEAKER: Richard Matthews (Univ. of Leeds)

TITLE: Taking Reinhardt’s Power Away

TIME: January 27 at 16:00 (CET)

PLACE: The Seminar will take place online at the following address:

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

(KGRC) research seminar talk on Thursday, January 28

Kurt Godel Research Center

1/25/2021 11:33:35

Research seminar Kurt Gödel Research Center Thursday, January 28 "Distributivity spectrum of forcing notions" Marlene Koelbing (KGRC), Wolfgang Wohofsky (KGRC) In our talk, we will introduce two different notions of a spectrum of distributivity of forcings. The first one is the fresh function spectrum, which is the set of regular cardinals lambda, such that the forcing adds a new function with domain lambda all whose initial segments are in the ground model. We will provide several examples as well as general facts how to compute the fresh function spectrum, also discussing what sets are realizable as a fresh function spectrum of a forcing. The second notion is the combinatorial distributivity spectrum, which is the set of possible regular heights of refining systems of maximal antichains without common refinement. We discuss the relation between the fresh function spectrum and the combinatorial distributivity spectrum. We consider the special case of P(omega)/fin (for which h is the minimum of the spectrum), and use a forcing construction to show that it is consistent that the combinatorial distributivity spectrum of P(omega)/fin contains more than one element. This is joint work with Vera Fischer. Time and Place Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

This Friday Talk: Corey Switzer (usual time)

Toronto Set Theory Seminar

1/25/2021 9:03:43

Hello everyone,

Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.

Here the speaker information:

Speaker: Corey Switzer, The Graduate Center, CUNY

Date and Time: Friday, January 29, 2021 - 1:30pm to 3:00pm

Title: Higher Dimensional Cardinal Characteristics for Sets of Real Valued Functions

Abstract:

Cardinal characteristics on the generalized Baire and Cantor spaces $\kappa^\kappa$ and $2^\kappa$ have recently generated significant interest. In this talk I will introduce a different generalization of cardinal characteristics, namely to the space of functions $f:\omega^\omega \to \omega^\omega$. Given an ideal $I$ on Baire space and a relation $R$ let us define $f R_I g$ for $f$ and $g$ functions from $\omega^\omega$ to $\omega^\omega$ if and only if $f(x) R g(x)$ for an $I$-measure one set of $x \in \omega^\omega$. By letting $I$ vary over the null ideal, the meager ideal and the bounded ideal; and $R$ vary over the relations $\leq^*$, $\neq^*$ and $\in^*$ we get 18 new cardinal characteristics by considering the bounding and dominating numbers for these relations. These new cardinals form a diagram of provable implications similar to the Cichoń diagram. They also interact in several surprising ways with the cardinal characteristics on $\omega$. For instance, they can be arbitrarily large in models of CH, yet they can be $\aleph_1$ in models where the continuum is arbitrarily large. They are bigger in the Sacks model than the Cohen model. I will introduce these cardinals, show some of the provable implications and discuss what is known about consistent inequalities, focusing on the $\mathfrak{b}$-numbers in well-known models such as the Cohen and Random model. This is joint work with Jörg Brendle.

Bio: Corey Bacal Switzer is currently a postdoctoral researcher at the Kurt Gödel Research Center For Mathematical Logic in the Mathematics Department of the University of Vienna working under Vera Fischer. He finished his PhD at the CUNY Graduate Center in New York in 2020. His research is in set theory, focusing on forcing, cardinal characteristics and infinite combinatorics

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

This Week in Logic at CUNY

1/24/2021 19:10:35

This Week in Logic at CUNY:

- - - - Monday, Jan 25, 2021 - - - -

- - - - Tuesday, Jan 26, 2021 - - - -

- - - - Wednesday, Jan 27, 2021 - - - -

- - - - Thursday, Jan 28, 2021 - - - -

- - - - Friday, Jan 29, 2021 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Jan 29, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Erin Carmody, Fordham University
The relationships between measurable and strongly compact cardinals: Part II

This talk is about the ongoing investigation of the relationships between measurable and strongly compact cardinals. I will present some of the history of the theorems in this theme, including Magidor's identity crisis, and give new results. The theorems presented are in particular about the relationships between strongly compact cardinals and measurable cardinals of different Mitchell orders. One of the main theorems is that there is a universe where $κ 1$ and $κ 2$ are the first and second strongly compact cardinals, respectively, and where $κ 1$ is least with Mitchell order 1, and $κ 2$ is the least with Mitchell order 2. Another main theorem is that there is a universe where $κ 1$ and $κ 2$ are the first and second strongly compact cardinals, respectively, with $κ 1$ the least measurable cardinal such that $o (κ 1) = 2$ and $κ 2$ the least measurable cardinal above $κ 1$ . This is a joint work in progress with Victoria Gitman and Arthur Apter.

Next Week in Logic at CUNY:

- - - - Monday, Feb 1, 2021 - - - -

- - - - Tuesday, Feb 2, 2021 - - - -

Models of Peano Arithmetic (MOPA)

Wednesday, Dec 9, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

James Walsh, Cornell University
Reducing omega-model reflection to iterated syntactic reflection

Two types of principles are commonly called “reflection principles” in reverse mathematics. According to syntactic reflection principles for T, every theorem of T (from some complexity class) is true. According to semantic reflection principles, every set belongs to some (sufficiently correct) model of T. We will present a connection between syntactic reflection and semantic reflection in second-order arithmetic: for any Pi^1_2 axiomatized theory T, every set is contained in an omega model of T if and only if every iteration of Pi^1_1 reflection for T along a well-ordering is Pi^1_1 sound. There is a thorough proof-theoretic understanding of the latter in terms of ordinal analysis. Accordingly, these reductions yield proof-theoretic analyses of omega-model reflection principles. This is joint work with Fedor Pakhomov.

- - - - Wednesday, Feb 3, 2021 - - - -

- - - - Thursday, Feb 4, 2021 - - - -

- - - - Friday, Feb 5, 2021 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Feb 5, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Andreas Blass, University of Michigan

TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Two talks by B. Siskind on February 9

Carnegie Mellon Logic Seminar

1/22/2021 21:22:24

TUESDAY, February 9, 2021 Mathematical logic seminar: 3:30 P.M., Online, Benjamin Siskind, University of California, Berkeley Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Order-preserving Martin’s Conjecture ABSTRACT: Martin’s Conjecture is a precise way of asserting that, up to equivalence, the only natural functions on the Turing degrees are the familiar ones: the constant functions, the identity, the Turing jump, and the transfinite iterates of the Turing jump. This conjecture is open even restricted to low-level Borel functions, but there have been partial results over the years which show it holds for classes of functions meeting requirements orthogonal to definability. Our recent result is that part of Martin’s Conjecture (lately called “part one”) holds for the class of order-preserving functions. In particular, it follows that the full Martin’s Conjecture holds for Borel order-preserving functions. We’ll talk about Martin’s Conjecture broadly and say something about this recent work. This is joint work with Patrick Lutz. TUESDAY, February 9, 2021 Set Theory Reading Group: 4:30 P.M., Online, Benjamin Siskind, University of California, Berkeley Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Measure-preserving functions on the Turing degrees ABSTRACT: One proof of part one of Martin’s Conjecture for order-preserving functions works for a bigger class of functions: those which are measure-preserving for the Martin measure, in the sense of ergodic theory. Looking at this class of functions brings out more set-theoretic aspects of Martin’s Conjecture. For example, part one of Martin’s Conjecture is equivalent to the non-existence of other non-principal ultrafilters on the Turing degrees Rudin-Keisler below the Martin measure. We’ll talk about the proof of part one of Martin’s Conjecture for this class of functions and some consequences. This is joint work with Patrick Lutz.

Tomorrow two talks (11 am and 1 30 pm)

Toronto Set Theory Seminar

1/21/2021 12:00:00

Hello everyone,

To start the semester we will have two talks: one at 11 am (Toronto time) and another at 1 30 pm (Toronto time).

Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Here the speakers information:

Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago

Date and Time: Friday, January 22, 2021 - 11am to 12:30pm

Title: Iteration, reflection, and singular cardinals

Abstract:

Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at $\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.

These principles are at odds with each other. The former is a compactness type principle. (Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object.) In contrast, failure of SCH is an instance of incompactness. The natural question is whether we can have both of these simultaneously. We show the answer is yes.

We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at $\aleph_{\omega}$ . This is joint work with Alejandro Poveda and Assaf Rinot.

Speaker: Marcos Mazari Armida, Carnagie Mellon University

Date and Time: Friday, January 22, 2021 - 1:30pm to 3pm

Title: Universal models in classes of abelian groups and modules
Abstract:

The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will study universal models in several classes of abelian groups and modules with respect to pure embeddings. In particular, we will present a complete solution below $\aleph_\omega$, with the exception of $\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals $\lambda$ such that there is a universal abelian p-group for purity of cardinality $\lambda$. The solution presented will use both model-theoretic and set-theoretic ideas.

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Two events on February 16

Carnegie Mellon Logic Seminar

1/19/2021 13:27:45

TUESDAY, February 16, 2021 Mathematical logic seminar: 3:30 P.M., Online, Aristotelis Panagiotopoulos, University of Muenster Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: The definable content of (co)homological invariants: Cech cohomology ABSTRACT: In this talk we will develop a framework for enriching various classical invariants of homological algebra and algebraic topology with additional descriptive set-theoretic information. The resulting "definable invariants" can be used for much finer classification than their purely algebraic counterparts. We will then illustrate how these ideas apply to the classical Cech cohomology theory, by introducing a new invariant for locally compact metrizable spaces up to homotopy equivalence which we call "definable cohomology". In strong contrast to its classical counterpart, this definable cohomology theory provides complete classification to homotopy classes of mapping telescopes of d-tori, and for homotopy classes of maps from mapping telescopes of d-tori to spheres. The latter problem was raised in the d=1 case by Borsuk and Eilenberg in 1936. This is joint work with Jeffrey Bergfalk and Martino Lupini. TUESDAY, February 16, 2021 Set Theory Reading Group: 4:30 P.M., Online, Aristotelis Panagiotopoulos, University of Muenster Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Ulam stability for quotients of abelian non-archimedean Polish groups ABSTRACT: Based on an earlier work of Shelah concerning the relationship of the continuum hypothesis to the cardinality of the set of automorphisms of $\mathcal{P}(\omega)/\mathrm{fin}$, Velickovic showed that if such an automorphism admits a Borel lift $\mathcal{P}(\omega)\to \mathcal{P}(\omega)$, then it is of a certain "trivial" form. Similarly, Kanovei and Reeken showed that if $N,M$ are countable dense subgroups of $\mathbb{R}$, then every homomorphism $\mathbb{R}/N\to \mathbb{R}/M$ with a Borel lift $\mathbb{R}\to \mathbb{R}$, is of a certain "trivial" form. Kanovei and Reeken asked whether quotients of the $p$-adic groups satisfy similar "Ulam stability" phenomena. In this talk, we will settle this question by providing Ulam-stability phenomena for definable homomorphisms $G/N\to H/M$ when $G,H$ are arbitrary abelian non-archimedean Polish groups and $N,M$ are Polishable subgroups. We will then illustrate how such rigidity results are in the heart of the definable cohomology theory which we developed in the previous talk. This is joint work with Jeffrey Bergfalk and Martino Lupini.

On Logic Seminar This Semester

NUS Logic Seminar

1/19/2021 2:58:41

Dear Attendees of the logic seminar, I would like to ask for volunteers who can give talks over Zoom at 17:00 hrs Singapore time, see http://www.comp.nus.edu.sg/~fstephan/logicseminar.html for free time-slots (currently all and I will put the names of those who reserve a slot into their preferred time-slot). Furthermore, for tomorrow, you might consider attending the talk of Brian Rabern from the University of Edinburgh at FASS on quantification as modelled by Frege and by Taski and the philosophical discussion will be moderated by Ben Blumson, NUS. Best regards, Frank `

(KGRC) research seminar talk on Thursday, January 21

Kurt Godel Research Center

1/18/2021 16:20:59

Research seminar Kurt Gödel Research Center Thursday, January 21 "Strong colourings over partitions" Juris Steprāns (York University, Toronto, Canada) The celebrated result of Todorcevic that $\aleph_1\not\rightarrow [\aleph_1]^2_{\aleph_1}$ provides a well known example of a strong colouring. A mapping $c:[\omega_1]^2\to \kappa$ is a strong colouring over a partition $p:[\omega_1]^2\to \omega$ if for every uncountable $X\subseteq \omega_1$ there is $n\in \omega$ such that the range of $c$ on $[X]^2\cap p^{-1}\{n\}$ is all of $\kappa$. I will discuss some recent work with A. Rinot and M. Kojman on negative results concerning strong colourings over partitions and their relation to classical results in this area. Time and Place Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

Barcelona Set theory Seminar

Barcelona Logic Seminar

1/17/2021 15:37:58

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

SPEAKER: Vera Fisher (Wien)

TITLE: Independent families in the countable and the uncountable

TIME: January 20 at 16:00 (CET)

PLACE: The Seminar will take place online at the following address:

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

BLAST 2021: June 9-13

Conference

1/16/2021

BLAST 2021 June 9-13, 2021 New Mexico State University, Las Cruces, NM, USA ONLINE Conference website: https://math.nmsu.edu/blast-2021/ Conference email: blast@nmsu.edu Submission link: https://easychair.org/conferences/?conf=blast2021 SCOPE BLAST is a conference series focusing on Boolean Algebras, Lattices, Algebraic Logic, Universal Algebra, Set Theory, Set-theoretic Topology, and Point-free Topology. The series circulates between different universities. The central BLAST web page, with links to past meetings, can be found here: http://math.colorado.edu/blast/ This year's installment of BLAST will take place at New Mexico State University. The scientific program will include invited lectures, tutorial lectures, two special sessions, and contributed talks. Due to the current pandemic, the conference will be entirely online. INVITED SPEAKERS: Aichinger, Erhard (Johannes Kepler University Linz) Carai, Luca (New Mexico State University) Celani, Sergio (National University of the Center of the Buenos Aires Province) Fisher, Vera (University of Vienna) Gehrke, Mai (University of Cote d’Azur, Nice) Hrusak, Michael (National Autonomous University of Mexico) Lapenta, Serafina (University of Salerno) Zamojska-Dzienio, Anna (Warsaw University of Technology) TUTORIALS: Bodirsky, Manuel (Dresden University of Technology) Dow, Alan (UNC Charlotte) Jung, Achim (University of Birmingham) SPECIAL SESSIONS: SPECIAL SESSION IN MEMORY OF W. CHARLES HOLLAND (1935—2020) AND JORGE MARTINEZ (1945—2020) Organizers: Rick Ball (University of Denver) and Warren McGovern (Florida Atlantic University) Speakers: Ball, Rick (University of Denver) Darnel, Michael (Indiana University South Bend) Droste, Manfred (University of Leipzig) Dube, Themba (University of South Africa) Dvurečenskij, Anatolij (Mathematical Institute, Slovak Academy of Sciences) Hager, Anthony (Wesleyan University) Marra, Vincenzo (University of Milan) McGovern, Warren (Florida Atlantic University) Schwartz, Niels (University of Passau) Tsinakis, Constantine (Vanderbilt University) SPECIAL SESSION ON STONE AND PRIESTLEY DUALITIES Speakers: Borlido, Célia (University of Coimbra) van Gool, Sam (University of Paris) Holliday, Wesley (UC Berkeley) Jibladze, Mamuka (Razmadze Mathematical Institute, Tbilisi State University) Melliès, Paul-André (University of Paris) Reggio, Luca (University of Oxford) Salvati, Sylvain (University of Lille) Tressl, Marcus (University of Manchester) CONTRIBUTED TALKS: Abstracts of contributed talks should be submitted through EasyChair: https://easychair.org/conferences/?conf=blast2021 Please indicate if you would like to submit to a special session. The abstract should not exceed 2 pages. IMPORTANT DATES: 11 April, 2021: Deadline for submitting abstracts of contributed talks 25 April, 2021: Notification of acceptance 9 June, 2021: Start of the conference 13 June, 2021: End of the conference LOCAL ORGANIZING COMMITTEE: Albee, Kempton (grad student) Bezhanishvili, Guram Carai, Luca (grad student) Harding, John Morandi, Pat Olberding, Bruce Peinado, Miguel (grad student) Raviprakash, Ranjitha (grad student) Shapirovsky, Ilya Sinclaire, Morgan (grad student)

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Tagged: Erhard Aichinger, Luca Carai, Sergio Celani, Vera Fisher, Mai Gehrke, Michael Hrusak, Serafina Lapenta, Anna Zamojska-Dzienio, Manuel Bodirsky, Alan Dow, Achim Jung, Rick Ball, Michael Darnel, Manfred Droste, Themba Dube, Anatolij Dvurečenskij, Anthony Hager, Vincenzo Marra, Warren McGovern, Niels Schwartz, Constantine Tsinakis, Célia Borlido, Sam van Gool, Wesley Holliday, Mamuka Jibladze, Paul-André Melliès, Luca Reggio, Sylvain Salvati, Marcus Tressl

Two events on February 2

Carnegie Mellon Logic Seminar

1/16/2021 10:43:13

TUESDAY, February 2, 2021 Mathematical logic seminar: 3:30 P.M., Online, Anush Tserunyan, McGill University Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Ergodic theorems along trees ABSTRACT: In the classical pointwise ergodic theorem for a probability measure preserving (pmp) transformation $T$, one takes averages of a given integrable function over the intervals $\{x, T(x), T^2(x), \hdots, T^n(x)\}$ in front of the point $x$. We prove a “backward” ergodic theorem for a countable-to-one pmp $T$, where the averages are taken over subtrees of the graph of T that are rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$). Surprisingly, this theorem yields forward ergodic theorems for countable groups, in particular, one for pmp actions of free groups of finite rank, where the averages are taken along subtrees of the standard Cayley graph rooted at the identity. This strengthens Bufetov’s theorem from 2000, which was the most general result in this vein. This is joint work with Jenna Zomback. TUESDAY, February 2, 2021 Set Theory Reading Group: 4:30 P.M., Online, Jenna Zomback, University of Illinois at Urbana-Champaign Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us] Meeting ID: 621 951 121 TITLE: Ergodic theorems along trees: the proofs ABSTRACT: In this continuation of the previous talk, we discuss a backward (inverse) ergodic theorem for a probability measure preserving (pmp) transformation $T$, where the averages are taken over subtrees of the graph of $T$ that are rooted at $x$ and lie behind $x$ (in the direction of $T^{-1}$). We will derive from it a new (forward) pointwise ergodic theorem for pmp actions of free groups of finite rank, where the averages are taken along subtrees of the standard Cayley graph rooted at the identity. We will then discuss a very short proof (due to Tserunyan) of the classical pointwise ergodic theorem, and, using this proof as an outline, we will sketch the proof of the backward ergodic theorem. This is joint work with Anush Tserunyan.

Two talks next week (January 22nd)

Toronto Set Theory Seminar

1/15/2021 18:29:14

There was a Typo in the last email. Here the correction:

Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago

Date and Time: Friday, January 22, 2021 - 11am to 12:30pm

Location: Online

Abstract: (In previous email)

Speaker: Marcos Mazari Armida, Carnagie Mellon University

Date and Time: Friday, January 22, 2021 - 1:30pm to 3pm

Title: Universal models in classes of abelian groups and modules
Abstract: (In previous email)

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

On Fri, Jan 15, 2021 at 5:19 PM Ivan Ongay Valverde <ivan.ongay.valverde@gmail.com> wrote:

Hello everyone,

To start the semester we will have two talks: one at 11 am (Toronto time) and another at 1 30 pm (Toronto time).

Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Here the speakers information:

Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago

Date and Time: Friday, January 22, 2021 - 11am to 12:30pm
Location: Online
Abstract:

Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at $\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.

These principles are at odds with each other. The former is a compactness type principle. (Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object.) In contrast, failure of SCH is an instance of incompactness. The natural question is whether we can have both of these simultaneously. We show the answer is yes.

We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at $\aleph_{\omega}$ . This is joint work with Alejandro Poveda and Assaf Rinot.

Speaker: Marcos Mazari Armida, Carnagie Mellon University

Date and Time: Friday, January 22, 2021 - 11am to 12:30pm

Title: Universal models in classes of abelian groups and modules
Abstract:

The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will study universal models in several classes of abelian groups and modules with respect to pure embeddings. In particular, we will present a complete solution below $\aleph_\omega$, with the exception of $\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals $\lambda$ such that there is a universal abelian p-group for purity of cardinality $\lambda$. The solution presented will use both model-theoretic and set-theoretic ideas.

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Two talks next week (January 22nd)

Toronto Set Theory Seminar

1/15/2021 18:19:40

Hello everyone,

To start the semester we will have two talks: one at 11 am (Toronto time) and another at 1 30 pm (Toronto time).

Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.

Here the speakers information:

Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, Chicago

Date and Time: Friday, January 22, 2021 - 11am to 12:30pm

Location: Online

Abstract:

Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at $\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.

These principles are at odds with each other. The former is a compactness type principle. (Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object.) In contrast, failure of SCH is an instance of incompactness. The natural question is whether we can have both of these simultaneously. We show the answer is yes.

We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at $\aleph_{\omega}$ . This is joint work with Alejandro Poveda and Assaf Rinot.

Speaker: Marcos Mazari Armida, Carnagie Mellon University

Date and Time: Friday, January 22, 2021 - 11am to 12:30pm

Title: Universal models in classes of abelian groups and modules
Abstract:

The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will study universal models in several classes of abelian groups and modules with respect to pure embeddings. In particular, we will present a complete solution below $\aleph_\omega$, with the exception of $\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals $\lambda$ such that there is a universal abelian p-group for purity of cardinality $\lambda$. The solution presented will use both model-theoretic and set-theoretic ideas.

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

(KGRC) research seminar talk on Thursday, January 14

Kurt Godel Research Center

1/11/2021 11:46:24

Research seminar Kurt Gödel Research Center Thursday, January 14 "Infinitary combinatorics and strong homology" Jeffrey Bergfalk (KGRC) Motivated by several recent advances, we will provide a research history of the main set-theoretic problems arising in the study of strong homology. As such, this talk will overlap with one on the same theme given in Paris-Lyon Logic Seminar last fall. We will presume no awareness in our audience either of strong homology or of that talk, but will aim in this one to provide, along with the necessary background, some sketch of the main ideas behind several recent arguments. This is an area in which simplicial principles and infinitary combinatorics come together. Its questions, at heart, have tended to be questions about higher-dimensional variants of classical set-theoretic concerns (like nontrivial coherence, $\Delta$ systems, etc.); these questions, in turn, increasingly appear to be of some interest in their own right. Time and Place Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

Barcelona Set theory Seminar

Barcelona Logic Seminar

1/11/2021 2:50:42

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

SPEAKER: Trevor M. Wilson (Miami Univ.)

TITLE: The large cardinal strength of Vopenka's Principle for trees and for rayless trees

TIME: January 13 at 16:00 (CET)

PLACE: The Seminar will take place online at the following address:

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Logic Seminar at NUS on Wednesday 13 Jan 2021 17:00 hrs - World Logic Day Special

NUS Logic Seminar

1/10/2021 23:33:48

Dear colleagues, This week's Logic Seminar on Wed 13 January 2021 at 17:00 hrs is an open session where, in light of the World Logic Day on Thursday, everyone is encouraged to give a 5 to 10 minutes presentation about his favourate result or results of his own work. In the case that you have no slides for this, feel free to share a Word file and type into it on Zoom. The result can be from any time where you have been working on logic, it should give the statement and contribution of the theorem. If you want to give a longer talk, we will schedule one in the next weeks. Best regards, Frank Here again the details: Wednesday 13 Jan 2021 17:00 hrs Singapore Time (+800) World Logic Seminar Special - Share your nicest results Discussion via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? You might reply with a short email to Frank Stephan (fstephan@comp.nus.edu.sg) and Yang Yue (matyangy@nus.edu.sg) if you follow our request for a short talk of 5 to 10 minutes, just for planning purposes. Best regards, Frank

(KGRC) research seminar talk on Thursday, December 17

Kurt Godel Research Center

12/14/2020 10:27:53

Research seminar Kurt Gödel Research Center Thursday, December 17 "Ramsey-like Operators" Peter Holy (University of Udine, Italy) Starting from measurability upwards, larger large cardinals are usually characterized by the existence of certain elementary embeddings of the universe, or dually, the existence of certain ultrafilters. However, below measurability, we have a somewhat similar picture when we consider certain embeddings with set-sized domain, or ultrafilters for small collections of sets. I will present some new results, and also review some older ones, showing that not only large cardinals below measurability, but also several related concepts can be characterized in such a way, and I will also provide a sample application of these characterizations. Time and Place Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

Barcelona Set Theory Seminar

Barcelona Logic Seminar

12/14/2020 2:36:18

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

SPEAKER: Victoria Gitman (CUNY)

TITLE: Characterizing large cardinals via abstract logics

TIME: December 16 at 16:00 (CET)

PLACE: The Seminar will take place online at the following address:

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

This Week in Logic at CUNY

12/13/2020 19:59:02

Hi everyone,

The coming week is final exams at CUNY, which will be followed by our winter break. This will be the last edition of "This Week in Logic" until the New Year. Have a happy holiday season!

Best,

Jonas

This Week in Logic at CUNY:

- - - - Monday, Dec 14, 2020 - - - -

Logic and Metaphysics Workshop

ST and All That: Philosophical Issues

For meeting information, please email: yweiss@gradcenter.cuny.edu

This will be a round table. Speakers (15 minutes each), followed by an open discussion:

Shay Logan (Kansas State)
Federico Pailos (Buenos Aires)
Dave Ripley (Monash)
Chris Scambler (NYU)

We may go on somewhat longer than the usual two hours if the discussion is productive. The meeting is open to all interested.

- - - - Tuesday, Dec 15, 2020 - - - -

- - - - Wednesday, Dec 16, 2020 - - - -

The New York City Category Theory Seminar

For meeting zoom details email N. Yanofsky.

Speaker: Arthur Parzygnat, IHES.

Date and Time: Wednesday December 16, 2020, 1:00 - 2:30 PM. ***NOTICE THE SPECIAL TIME***, on Zoom.

Title: A functorial characterization of classical and quantum entropies.

Abstract: Entropy appears as a useful concept in a wide variety of academic disciplines. As such, one would suspect that category theory would provide a suitable language to encompass all or most of these definitions. The Shannon entropy has recently been given a characterization as a certain affine functor by Baez, Fritz, and Leinster. This characterization is the only characterization I know of that uses linear assumptions (as opposed to additive, exponential, logarithmic, etc). Here, we extend that characterization to include the von Neumann entropy as well as highlight the new categorical structures that arise when trying to do so. In particular, we introduce Grothendieck fibrations of convex categories, and we review the notion of a disintegration, which is a key part of conditional probability and Bayesian statistics and plays a crucial role in our characterization theorem. The characterization of Baez, Fritz, and Leinster interprets Shannon entropy in terms of the information loss associated to a deterministic process, which is possible since the entropy difference associated to such a process is always non-negative. This fails for quantum entropy, and has important physical consequences.

References:
Paper (and references therein)
Paper (original paper of Baez, Fritz, and Leinster)

- - - - Thursday, Dec 17, 2020 - - - -

Philog Seminar
Thursday, December 17, 6:30 PM EST
Barbara H. Partee, Department of Linguistics, University of Massachusetts Amherst
Language and Logic: Ideas and Controversies in the History of Formal Semantics
(As a very senior and accomplished linguist she is the right person to tell us about formal semantics.)

Brief abstract: The history of formal semantics and pragmatics over the last 50 years is a story of collaboration among linguists, logicians, and philosophers. Since this talk is for a seminar in philosophy, logic, and games, and I’m a linguist, I’ll emphasize aspects of the pre-history and history of formal semantics that concern the relation between language and logic, not presupposing knowledge of linguistics.

Zoom link will be posted on https://philog.arthurpaulpedersen.org/

- - - - Friday, Dec 18, 2020 - - - -

Next Week in Logic at CUNY:

- - - - Monday, Dec 21, 2020 - - - -

- - - - Tuesday, Dec 22, 2020 - - - -

- - - - Wednesday, Dec 23, 2020 - - - -

- - - - Thursday, Dec 24, 2020 - - - -

- - - - Friday, Dec 25, 2020 - - - -

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

(KGRC) research seminar talk on Thursday, December 10

Kurt Godel Research Center

12/7/2020 10:26:42

Research seminar Kurt Gödel Research Center Thursday, December 10 "Invariant Ideal Axiom" Michael Hrušák (UNAM, Mexico City, Mexico) We shall introduce a consistent set-theoretic axiom which has a profound impact on convergence properties in topological groups. As an application we show that consistently (consequence of IIA) every countable sequential group is either metrizable or $k_\omega$. Time and Place Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

This Week in Logic at CUNY

12/6/2020 22:22:28

This Week in Logic at CUNY:

- - - - Monday, Dec 7, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, December 7, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Jennifer McDonald (CUNY)

Title: Essential Structure and Apt Causal Models

Abstract: A promising account of actual causation – the causal relation holding between two token events – uses the language of structural equation models (SEMs). Such an account says, roughly, that actual causation holds between two token events when there is a suitable model according to which (1) the two events occur; and (2) intervening on the model to change the value of the variable that represents the cause changes the value of the variable that represents the effect (Halpern & Pearl, 2005; Hitchcock, 2001; Weslake, 2015; Woodward, 2003). Of course, this calls for an account of when a model is suitable – or, apt. Although initially bracketed, this issue is increasingly pressing; in part due to the recently discovered problem of structural isomorphs (Hall 2007; Hitchcock 2007a; Blanchard and Schaffer 2017; Menzies 2017). This paper offers a unified analysis of two aptness requirements from the literature – those enjoining us to include essential structure and avoid unstable models. While successfully invoked by Blanchard and Schaffer (2017) to resolve the problem of structural isomorphs, these requirements are unilluminating as they stand. My paper synthesizes them into a single aptness requirement that, I claim, gets to the heart of what’s representationally required of a causal model for capturing actual causation.

- - - - Tuesday, Dec 8, 2020 - - - -

- - - - Wednesday, Dec 9, 2020 - - - -

Models of Peano Arithmetic (MOPA)
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Wednesday, Dec 9, 3pm
Konrad Zdanowski, Cardinal Stefan Wyszynski University in Warsaw

Truth predicate for $Δ 0$ formulas and PSPACE computations

We consider a bounded arithmetic in Buss's language enriched with a predicate Tr which is assumed to be a truth definition for bounded sentences. Among other things we assume polynomial induction for $Σ b 1 (Tr)$ formulas. We show that such an arithmetic captures PSPACE. We prove a witnessing theorem for such an arithmetic by an interpretation of free-cuts free proofs of strict $Σ 1, b 1$ in $U 1, * 2$ , a canonical second order arithmetic capturing PSPACE. It follows that the problem of the existence of a truth definition for $Δ 0$ sentences without the totality of $exp$ might be more about separating subexponential time alternation hierarchies from PSPACE.

The presentation is based on the following article: Konrad Zdanowski, Truth definition for $Δ 0$ formulas and PSPACE computations, Fundamenta Mathematicae 252(2021) , 1-38.

The New York City Category Theory Seminar

For meeting zoom details email N. Yanofsky.

Speaker: Dan Shiebler, Oxford University.
Date and Time: Wednesday December 9, 2020, 7:00 - 8:30 PM., on Zoom.
Title: Functorial Manifold Learning and Overlapping Clustering.

Abstract: We adapt previous research on functorial clustering and topological unsupervised learning to develop a functorial perspective on manifold learning algorithms. Our framework characterizes a manifold learning algorithm in terms of the loss function that it optimizes, which allows us to focus on the algorithm's objective rather than the details of the learning process. We demonstrate that we can express several state of the art manifold learning algorithms, including Laplacian Eigenmaps, Metric Multidimensional Scaling, and UMAP, as functors in this framework. This functorial perspective allows us to reason about the invariances that these algorithms preserve and prove refinement bounds on the kinds of loss functions that any such functor can produce. Finally, we experimentally demonstrate how this perspective enables us to derive and analyze novel manifold learning algorithms.

- - - - Thursday, Dec 10, 2020 - - - -

- - - - Friday, Dec 11, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Dec 11, 11am

The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Dima Sinapova, University of Chicago

Iteration, reflection, and singular cardinals

There is an inherent tension between stationary reflection and the failure of the singular cardinal hypothesis (SCH). The former is a compactness type principle that follows from large cardinals. Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object. In contrast, failure of SCH is an instance of incompactness.

Two classical results of Magidor are:
(1) from large cardinals it is consistent to have reflection at $ℵ ω + 1$ , and
(2) from large cardinals it is consistent to have the failure of SCH at $ℵ ω$ .

As these principles are at odds with each other, the natural question is whether we can have both. We show the answer is yes.

We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at $ℵ ω$ by interleaving collapses. This is joint work with Alejandro Poveda and Assaf Rinot.

Next Week in Logic at CUNY:

- - - - Monday, Dec 14, 2020 - - - -

- - - - Tuesday, Dec 15, 2020 - - - -

- - - - Wednesday, Dec 16, 2020 - - - -

The New York City Category Theory Seminar

For meeting zoom details email N. Yanofsky.

Speaker: Arthur Parzygnat, IHES.

Date and Time: Wednesday December 16, 2020, 1:00 - 2:30 PM. ***NOTICE THE SPECIAL TIME***, on Zoom.

Title: A functorial characterization of classical and quantum entropies.

Abstract: Entropy appears as a useful concept in a wide variety of academic disciplines. As such, one would suspect that category theory would provide a suitable language to encompass all or most of these definitions. The Shannon entropy has recently been given a characterization as a certain affine functor by Baez, Fritz, and Leinster. This characterization is the only characterization I know of that uses linear assumptions (as opposed to additive, exponential, logarithmic, etc). Here, we extend that characterization to include the von Neumann entropy as well as highlight the new categorical structures that arise when trying to do so. In particular, we introduce Grothendieck fibrations of convex categories, and we review the notion of a disintegration, which is a key part of conditional probability and Bayesian statistics and plays a crucial role in our characterization theorem. The characterization of Baez, Fritz, and Leinster interprets Shannon entropy in terms of the information loss associated to a deterministic process, which is possible since the entropy difference associated to such a process is always non-negative. This fails for quantum entropy, and has important physical consequences.

References:
Paper (and references therein)
Paper (original paper of Baez, Fritz, and Leinster)

- - - - Thursday, Dec 17, 2020 - - - -

- - - - Friday, Dec 18, 2020 - - - -

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Barcelona Set Theory Seminar

Barcelona Logic Seminar

12/4/2020 6:51:20

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

SPEAKER: Neil Barton (University of Konstanz)

TITLE: Intensional classes and intuitionistic topoi

TIME: December 9 at 16:00 (CET)

PLACE: The Seminar will take place online at the following address:

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

Set theory in the UK workshop, online, December 4

Conference

12/1/2020

The next Set Theory in the UK workshop will take place online on Friday, 4 December 2020, from 9.30am-2pm. Please see the meeting's website http://www1.maths.leeds.ac.uk/~pmtadb/STUK6/STUK6.html for more information. How to participate: Information how to obtain a login will be available on the conference website soon. Please find this information in advance, on the day before the meeting. 09.30-09.55 Yair Hayut (Hebrew University of Jerusalem): Generics via ultrapowers 10.00-10.50 Arno Pauly (Swansea University): Luzin's (N) and randomness reflection 11.00-11.50 Peter Holy (University of Udine): Ramsey-like operators lunch break 13.30-13.55 Jiachen Yuan (University of East Anglia): Indestructibility of supercompactness and large cardinals Titles and abstracts: Yair Hayut: Generics via ultrapowers Bukovský and Dehornoy observed (independently) that there is a generic for the Prikry forcing over the iterated ultrapower by the measure. I will show how one can use this fact in order to derive (without referring to the forcing) many interesting properties of the generic extension. Arno Pauly: Luzin's (N) and randomness reflection Peter Holy: Ramsey-like operators Starting from measurability upwards, larger large cardinals are usually characterized by the existence of certain elementary embeddings of the universe, or dually, the existence of certain ultrafilters. However, below measurability, we have a somewhat similar picture when we consider certain embeddings with set-sized domain, or ultrafilters for small collections of sets. I will present some new results, and also review some older ones, showing that not only large cardinals below measurability, but also several related concepts can be characterized in such a way, and I will also provide a sample application of these characterizations. Jiachen Yuan: Indestructibility of supercompactness and large cardinals It is well known that "there is a supercompact cardinal which is immune to any $\kappa-$directed closed set forcing" is relatively consistent with "there is a supercompact cardinal". We also know that there is no analogue of such a theorem to any large cardinal stronger than extendible. In fact, provably in $ZFC$ such large cardinal properties will be destroyed by any $\kappa-$directed closed set forcing. For larger cardinals, according to a theorem of Usuba, they can not survive in any set-forcing extension which is not equivalent to a small forcing. However, it was not known if it is possible to have such a large cardinal notion with its supercompactness indestructible. It turns out that this is true for a lot of large cardinals by forcing from a ground model with the same strength. See you at the meeting! Andrew Brooke-Taylor, Asaf Karagila and Philipp Schlicht

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Tagged: Yair Hayut, Arno Pauly, Peter Holy, Jiachen Yuan

Talk this Friday 2 hours-long (1 30 pm Toronto time)

Toronto Set Theory Seminar

11/30/2020 13:27:39

Hello all,

This week:

Date: Friday December 4, 1.30pm (2 hours long)

location: Online
Please use the following link and fill the form (every week) to enter
the meeting. This form helps the Field Institute to know statistical
data about attendance.

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Speaker: Thomas Daniells Gilton

Affiliation: Department of Mathematics, The University of Pittsburgh

Title: The Abraham-Rubin-Shelah Open Coloring Axiom with a Large
Continuum

Abstract:

Open Coloring Axioms may be viewed as consistent generalizations of
Ramsey's Theorem to $\omega_1$ in which topological restrictions are
placed on the colorings. The first of these, denoted
$\mathsf{OCA}_{ARS}$, appeared in the 1985 paper by Abraham, Rubin, and
Shelah. There the authors showed that $\mathsf{OCA}_{ARS}$ is consistent
with $\mathsf{ZFC}$. To ensure that the posets which add the homogeneous
sets satisfy the c.c.c., they construct a type of ``diagonalization"
object (for a continuous coloring $\chi$) called a \emph{Preassignment
of Colors}, which guides the forcing to add the $\chi$-homogeneous sets.

However, the only known constructions of effective preassignments
require the $\mathsf{CH}$. Since a forcing iteration of $\aleph_1$-sized
posets all of whose proper initial segments satisfy the $\mathsf{CH}$
results in a model in which $2^{\aleph_0}$ is at most $\aleph_2$, this
leads naturally to the question of whether $\mathsf{OCA}_{ARS}$ is
consistent, say, with $2^{\aleph_0}=\aleph_3$.

In joint work with Itay Neeman, we answer this question in the
affirmative. In light of the $\mathsf{CH}$ obstacle, we only construct
names for preassignments with respect to a small class $\mathcal{A}$ of
$\mathsf{CH}$-preserving iterations. However, our preassignments are
powerful enough to work even over models in which the $\mathsf{CH}$
fails.

Our final forcing is built by combining the members of $\mathcal{A}$
into a new type of forcing, called a \emph{Partition Product}. A
partition product is a type of restricted memory iteration with
isomorphism and coherent-overlap conditions on the memories. In
particular, each ``memory" is isomorphic to a member of $\mathcal{A}$.

In this talk, we will describe in some detail the definition of a
Partition Product. We will then discuss how to construct more general
preassignments than those used by Abraham, Rubin, and Shelah, gesturing
at the end towards the full construction which we use for our theorem.

========================================

Speaker Bio:

I am a Visiting Assistant Professor in the department of Mathematics at
the University of Pittsburgh, having graduated from UCLA in the Fall of
2019 under the supervision of Itay Neeman. I am interested in questions
about what combinatorial principles determine the size of the continuum,
as well as in questions about the tension between compactness and
incompactness principles in set theory. I reside in Pittsburgh with my
wife, Marian (who is a philosopher of physics), with our indefatigable
toddler Zoe, and with our two cats.

See you then!

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

(KGRC) research seminar talk on December 3

Kurt Godel Research Center

11/30/2020 10:32:23

Research seminar Kurt Gödel Research Center Thursday, December 3 "On logics that make a bridge from the Discrete to the Continuous" Mirna Džamonja (CNRS & Panthéon Sorbonne, Paris, France and Czech Academy of Sciences, Prague) The talk starts with a surveys of some recent connections between logic and discrete mathematics. Then we discuss logics which model the passage between an infinite sequence of finite models to an uncountable limiting object, such as is the case in the context of graphons. Of particular interest is the connection between the countable and the uncountable object that one obtains as the union versus the combinatorial limit of the same sequence. We compare such logics and discuss some consequences of such comparisons, as well as some hopes for further results in this research project. Time and Place Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

This Week in Logic at CUNY

11/29/2020 21:56:09

This Week in Logic at CUNY:

- - - - Monday, Nov 23, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 23, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Behnam Zolghadr (LMU Munich)

Title: How to Abū Hāšim Meinong

Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.

- - - - Tuesday, Nov 24, 2020 - - - -

Computational Logic Seminar

Tuesday November 24, 2-4pm
Ask Sergei Artemov for the (usual) link, unless you already have it.

Speaker: Stepan Kuznetsov, Steklov Mathematical Institute, Russian Academy of Sciences
Title: Ad hoc algebraic models for non-standard Kleene stars

Abstract: Kleene iteration, or Kleene star, is one of the most intriguing algebraic operations appearing in theoretical computer science. In most conventional models, the Kleene star a* is interpreted as the union (limit) of n-th powers of a. In relational structures, this corresponds to reflexive-transitive closure, in language models it is iteration of languages, and so on. Such interpretation of the Kleene star is called -continuous. However, the usual axiomatization of the Kleene star using induction principles (as opposed to the omega-rule), is essentially weaker and, thus, admits a broader class of models. Existence of nonstandard, non--continuous models can be easily proved non-constructively. However, in order to use such models for studying substructural logics with Kleene star one has to construct them explicitly. In this talk, we show two of such models, constructed for proving some facts about derivability in extensions of the Lambek calculus with the Kleene star. Both models are ad hoc algebraic constructions, and we do not yet know whether they could fit in a natural family of models.

The talk is based on my AiML 2018 and AiML 2020 papers

- - - - Wednesday, Nov 25, 2020 - - - -

- - - - Thursday, Nov 26, 2020 - - - -

THANKSGIVING RECESS

- - - - Friday, Nov 27, 2020 - - - -

THANKSGIVING RECESS

Next Week in Logic at CUNY:

- - - - Monday, Nov 30, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 30, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Mircea Dumitru (Bucharest)

Title: A Free Logic for Fictionalism

Abstract: In Reference without Referents, Mark Sainsbury aims to provide an account of reference that honours the common-sense view that sentences containing empty names like “Sherlock Holmes”, “Vulcan”, and “Santa Claus” are entirely intelligible, and that many such sentences — “Vulcan doesn’t exist”, “Many children believe that Santa Claus will give them presents at Christmas”, etc.— are literally true. Sainsbury’s account endorses the Davidsonian program in the theory of meaning, and combines this with a commitment to Negative Free Logic, which holds that all simple sentences containing empty names are false. In my talk, I pose a number of problems for this account. In particular, I question the ability of Negative Free Logic to make appropriate sense of the truth of familiar sentences containing empty names, including negative existential claims like “Vulcan doesn’t exist”.

Note: this is based on joint work with Frederick Kroon (Auckland).

- - - - Tuesday, Dec 1, 2020 - - - -

Computational Logic Seminar

Tuesday December 1, 2-4pm
Ask Sergei Artemov for the (usual) link, unless you already have it.

Speaker: Rohit Parikh, Brooklyn College and CUNY Graduate Center
Title: TOPOLOGY AND EPISTEMIC LOGIC

Abstract. We present the main ideas behind a number of logical systems for reasoning about points and sets that incorporate knowledge-theoretic ideas, and also the main results about them. Some of our discussions will be about applications of modal ideas to topology, and some will be on applications of topological ideas in modal logic, especially in epistemic logic.

In the former area, we would like to present the basic ideas and results of topologic, the study of two-sorted bimodal logical systems interpreted on subset spaces; these are arbitrary sets with collections of subsets called opens. Many of the papers in this field deal with questions of axiomatizing the logics of particular classes of subset spaces determined by conditions on the “opens”, such as being closed under intersection, being topologies, or satisfying various chain conditions.

Work in this area has been done by RP as well as Larry Moss (Indiana), Andrew Dabrowski (Indiana), K Georgatos (CUNY), Angela Weiss (CUNY), Chris Steinsvold (CUNY), Bernhard Heinemann (Hagen), Can Baskent (CUNY) and many others.

- - - - Wednesday, Dec 2, 2020 - - - -

- - - - Thursday, Dec 3, 2020 - - - -

- - - - Friday, Dec 4, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Dec 4, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Zach Norwood, University of Michigan

TBA

Next Week in Logic at CUNY:

- - - - Monday, Dec 7, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, December 7, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Jennifer McDonald (CUNY)

Title: Essential Structure and Apt Causal Models

Abstract: A promising account of actual causation – the causal relation holding between two token events – uses the language of structural equation models (SEMs). Such an account says, roughly, that actual causation holds between two token events when there is a suitable model according to which (1) the two events occur; and (2) intervening on the model to change the value of the variable that represents the cause changes the value of the variable that represents the effect (Halpern & Pearl, 2005; Hitchcock, 2001; Weslake, 2015; Woodward, 2003). Of course, this calls for an account of when a model is suitable – or, apt. Although initially bracketed, this issue is increasingly pressing; in part due to the recently discovered problem of structural isomorphs (Hall 2007; Hitchcock 2007a; Blanchard and Schaffer 2017; Menzies 2017). This paper offers a unified analysis of two aptness requirements from the literature – those enjoining us to include essential structure and avoid unstable models. While successfully invoked by Blanchard and Schaffer (2017) to resolve the problem of structural isomorphs, these requirements are unilluminating as they stand. My paper synthesizes them into a single aptness requirement that, I claim, gets to the heart of what’s representationally required of a causal model for capturing actual causation.

- - - - Tuesday, Dec 8, 2020 - - - -

- - - - Wednesday, Dec 9, 2020 - - - -

- - - - Thursday, Dec 10, 2020 - - - -

- - - - Friday, Dec 11, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Dec 11, 11am

The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Dima Sinapova, University of Chicago

TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Barcelona Set Theory Seminar

Barcelona Logic Seminar

11/29/2020 5:10:28

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

SPEAKER: Toby Meadows (UC Irvine)

TITLE: What set theory could not be

TIME: December 2 at 16:00 (CET)

PLACE: The Seminar will take place online at the following address:

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Reminder: Talk tomorrow at 1 30

Toronto Set Theory Seminar

11/26/2020 14:29:00

Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.

Speaker: Sandra Müller, University of Vienna

Date and Time: Friday, November 27, 2020 - 1:30pm to 3:00pm

Location: https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Abstract:

The study of inner models was initiated by Gödel’s analysis of the constructible universe L

. Later, it became necessary to study canonical inner models with large cardinals, e.g. measurable cardinals, strong cardinals or Woodin cardinals, which were introduced by Jensen, Mitchell, Steel, and others. Around the same time, the study of infinite two-player games was driven forward by Martin’s proof of analytic determinacy from a measurable cardinal, Borel determinacy from ZFC, and Martin and Steel’s proof of levels of projective determinacy from Woodin cardinals with a measurable cardinal on top. First Woodin and later Neeman improved the result in the projective hierarchy by showing that in fact the existence of a countable iterable model, a mouse, with Woodin cardinals and a top measure suffices to prove determinacy in the projective hierarchy.

This opened up the possibility for an optimal result stating the equivalence between local determinacy hypotheses and the existence of mice in the projective hierarchy, just like the equivalence of analytic determinacy and the existence of x♯

for every real x

which was shown by Martin and Harrington in the 70’s. The existence of mice with Woodin cardinals and a top measure from levels of projective determinacy was shown by Woodin in the 90’s. Together with his earlier and Neeman’s results this estabilishes a tight connection between descriptive set theory in the projective hierarchy and inner model theory.

In this talk, we will outline some of the main results connecting determinacy hypotheses with the existence of mice with large cardinals and discuss a number of more recent results in this area.

On Friday Dec. 4th we will have Thomas Gilton. Please, also see the webpage http://www.fields.utoronto.ca/activities/20-21/set-theory-seminar

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Sandra Muller Talk this Friday 1 30 pm

Toronto Set Theory Seminar

11/23/2020 13:27:26

Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Speaker: Sandra Müller, University of Vienna

Date and Time: Friday, November 27, 2020 - 1:30pm to 3:00pm

Location: https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Abstract:

The study of inner models was initiated by Gödel’s analysis of the constructible universe L

. Later, it became necessary to study canonical inner models with large cardinals, e.g. measurable cardinals, strong cardinals or Woodin cardinals, which were introduced by Jensen, Mitchell, Steel, and others. Around the same time, the study of infinite two-player games was driven forward by Martin’s proof of analytic determinacy from a measurable cardinal, Borel determinacy from ZFC, and Martin and Steel’s proof of levels of projective determinacy from Woodin cardinals with a measurable cardinal on top. First Woodin and later Neeman improved the result in the projective hierarchy by showing that in fact the existence of a countable iterable model, a mouse, with Woodin cardinals and a top measure suffices to prove determinacy in the projective hierarchy.

This opened up the possibility for an optimal result stating the equivalence between local determinacy hypotheses and the existence of mice in the projective hierarchy, just like the equivalence of analytic determinacy and the existence of x♯

for every real x

which was shown by Martin and Harrington in the 70’s. The existence of mice with Woodin cardinals and a top measure from levels of projective determinacy was shown by Woodin in the 90’s. Together with his earlier and Neeman’s results this estabilishes a tight connection between descriptive set theory in the projective hierarchy and inner model theory.

In this talk, we will outline some of the main results connecting determinacy hypotheses with the existence of mice with large cardinals and discuss a number of more recent results in this area.

On Friday Dec. 4th we will have Thomas Gilton. Please, also see the webpage http://www.fields.utoronto.ca/activities/20-21/set-theory-seminar

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

(KGRC) research seminar talk on Thursday, November 26

Kurt Godel Research Center

11/23/2020 9:54:24

Research seminar Kurt Gödel Research Center Thursday, November 26 "Convergence of Borel measures and filters on omega" Damian Sobota (KGRC) The celebrated Josefson--Nissenzweig theorem asserts, under certain interpretations, that for every infinite compact space K there exists a sequence of normalized signed Borel measures on K which converges to 0 with respect to every continuous real-valued function (i.e. the corresponding integrals converge to 0). We showed that in the case of products of two infinite compact spaces K and L one can construct such a sequence of measures with an additional property that every measure has finite support---let us call such a sequence ``an fsJN-sequence'' (i.e. a finitely supported Josefson--Nissenzweig sequence). We then studied the case when the spaces K and L are only pseudocompact and we proved in ZFC that if the product of K and L is pseudocompact, then it also admits an fsJN-sequence. On the other hand, we showed that under the Continuum Hypothesis, or Martin's axiom, or even some weaker set-theoretic assumptions concerning weak P-points, there exists a pseudocompact space X such that its square is not pseudocompact and it does not admit any fsJN-sequences. During my talk I will discuss these as well as other results concerning the topic and obtained during a joint work with various combinations of J. Kakol, W. Marciszewski and L. Zdomskyy. Time and Place Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

This Week in Logic at CUNY

11/22/2020 20:32:48

This Week in Logic at CUNY:

- - - - Monday, Nov 23, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 23, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Behnam Zolghadr (LMU Munich)

Title: How to Abū Hāšim Meinong

Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.

- - - - Tuesday, Nov 24, 2020 - - - -

Computational Logic Seminar

Tuesday November 24, 2-4pm
Ask Sergei Artemov for the (usual) link, unless you already have it.

Speaker: Stepan Kuznetsov, Steklov Mathematical Institute, Russian Academy of Sciences
Title: Ad hoc algebraic models for non-standard Kleene stars

Abstract: Kleene iteration, or Kleene star, is one of the most intriguing algebraic operations appearing in theoretical computer science. In most conventional models, the Kleene star a* is interpreted as the union (limit) of n-th powers of a. In relational structures, this corresponds to reflexive-transitive closure, in language models it is iteration of languages, and so on. Such interpretation of the Kleene star is called -continuous. However, the usual axiomatization of the Kleene star using induction principles (as opposed to the omega-rule), is essentially weaker and, thus, admits a broader class of models. Existence of nonstandard, non--continuous models can be easily proved non-constructively. However, in order to use such models for studying substructural logics with Kleene star one has to construct them explicitly. In this talk, we show two of such models, constructed for proving some facts about derivability in extensions of the Lambek calculus with the Kleene star. Both models are ad hoc algebraic constructions, and we do not yet know whether they could fit in a natural family of models.

The talk is based on my AiML 2018 and AiML 2020 papers

- - - - Wednesday, Nov 25, 2020 - - - -

- - - - Thursday, Nov 26, 2020 - - - -

THANKSGIVING RECESS

- - - - Friday, Nov 27, 2020 - - - -

THANKSGIVING RECESS

Next Week in Logic at CUNY:

- - - - Monday, Nov 30, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 30, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Mircea Dumitru (Bucharest)

Title: A Free Logic for Fictionalism

Abstract: In Reference without Referents, Mark Sainsbury aims to provide an account of reference that honours the common-sense view that sentences containing empty names like “Sherlock Holmes”, “Vulcan”, and “Santa Claus” are entirely intelligible, and that many such sentences — “Vulcan doesn’t exist”, “Many children believe that Santa Claus will give them presents at Christmas”, etc.— are literally true. Sainsbury’s account endorses the Davidsonian program in the theory of meaning, and combines this with a commitment to Negative Free Logic, which holds that all simple sentences containing empty names are false. In my talk, I pose a number of problems for this account. In particular, I question the ability of Negative Free Logic to make appropriate sense of the truth of familiar sentences containing empty names, including negative existential claims like “Vulcan doesn’t exist”.

Note: this is based on joint work with Frederick Kroon (Auckland).

- - - - Tuesday, Dec 1, 2020 - - - -

- - - - Wednesday, Dec 2, 2020 - - - -

- - - - Thursday, Dec 3, 2020 - - - -

- - - - Friday, Dec 4, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Dec 4, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Zach Norwood, University of Michigan

TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Barcelona Set Theory Seminar

Barcelona Logic Seminar

11/21/2020 11:38:02

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

SPEAKER: Andrew Brooke-Taylor (Leeds)

TITLE: Categorifying Borel Reducibility

TIME: November 25 at 16:00 (CET)

PLACE: The Seminar will take place online at the following address:

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Reminder of tomorrow's talk 1 30 pm

Toronto Set Theory Seminar

11/19/2020 13:00:00

Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.

Speaker: Andrea Medini, University of Vienna

Date and Time: Friday, November 20, 2020 - 1:30pm to 3:00pm

Location: https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Abstract:

Wadge theory provides an exhaustive analysis of the topological complexity of the subsets of a zero-dimensional Polish space. Fons van Engelen pioneered its applications to topology by obtaining a classification of the zero-dimensional homogeneous Borel spaces (recall that a space X is homogeneous if for all x,y∈X there exists a homeomorphism h:X⟶X such that h(x)=y).

As a corollary, he showed that all such spaces (apart from trivial exceptions) are in fact strongly homogeneous (recall that a space X is strongly homogeneous if all non-empty clopen subspaces of X are homeomorphic to each other).

In a joint work with the other members of the “Wadge Brigade” (namely, Raphaël Carroy and Sandra Müller), we showed that this last result extends beyond the Borel realm if one assumes AD. We intend to sketch the proof of this theorem, with a view towards a complete classification of the zero-dimensional homogeneous spaces under AD.

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Andrea Medina talk-Toronto Set Theory Seminar

Toronto Set Theory Seminar

11/16/2020 12:54:27

I send you the information for this week's talk.

Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Speaker: Andrea Medini, University of Vienna

Date and Time: Friday, November 20, 2020 - 1:30pm to 3:00pm

Location: https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

Abstract:

Wadge theory provides an exhaustive analysis of the topological complexity of the subsets of a zero-dimensional Polish space. Fons van Engelen pioneered its applications to topology by obtaining a classification of the zero-dimensional homogeneous Borel spaces (recall that a space X is homogeneous if for all x,y∈X there exists a homeomorphism h:X⟶X such that h(x)=y).

As a corollary, he showed that all such spaces (apart from trivial exceptions) are in fact strongly homogeneous (recall that a space X is strongly homogeneous if all non-empty clopen subspaces of X are homeomorphic to each other).

In a joint work with the other members of the “Wadge Brigade” (namely, Raphaël Carroy and Sandra Müller), we showed that this last result extends beyond the Borel realm if one assumes AD. We intend to sketch the proof of this theorem, with a view towards a complete classification of the zero-dimensional homogeneous spaces under AD.

Next week we will have

Sandra Müller, University of Vienna

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

(KGRC) research seminar talk on Thursday, November 19

Kurt Godel Research Center

11/16/2020 10:41:08

Research seminar Kurt Gödel Research Center Thursday, November 19 "Local club condensation in extender models" Gabriel Fernandes (Bar-Ilan University, Ramat Gan, Israel) Local club condensation is a condensation principle defined by Friedman and Holy. It is a theorem due to Friedman and Holy that local club condensation holds in most of the extender models that are weakly iterable. We prove that in any weakly iterable extender model with $\lambda$-indexing, given a cardinal $\kappa$, the sequence $\langle L_\alpha [E] \mid \alpha < \kappa^{++} \rangle$ witnesses local club condensation on the interval $(\kappa^+ , \kappa^{++})$ iff $\kappa$ is not a subcompact cardinal in $L[E]$. We also prove that if $\kappa$ is subcompact, then there is no sequence $\langle M_\alpha \mid \alpha < \kappa^{++} \rangle \in L[E]$ with $M_\kappa = (H_\kappa)^{L[E]}$ and $M_{\kappa^{++}} = (H_{\kappa^{++}})^{L[E]}$ which witnesses local club condensation in $(\kappa^+ , \kappa^{++})$. Using the equivalence between subcompact cardinals and $\neg\square_\kappa$, due to Schimmerling and Zeman, it follows that $\square_\kappa$ holds iff the sequence $\langle L_\alpha [E] \mid \alpha < \kappa^{++} \rangle$ witnesses local club condensation on the interval $(\kappa^+ , \kappa^{++})$. Time and Place Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

This Week in Logic at CUNY

11/15/2020 18:30:13

This Week in Logic at CUNY:

- - - - Monday, Nov 16, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 16, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Speaker: Nick Stang (Toronto)

Title: Hegel’s Logic as Logic and as Metaphysics

Abstract: In the Encyclopaedia Logic Hegel claims that logic “coincides with” metaphysics (§24). In this talk, I will explain why Hegelian logic (the science of thinking) is identical with metaphysics (the science of being). Along the way, I will also shed light on two of the most obscure aspects of Hegel’s logic: that it involves “movement” and that this movement works by the identification, and resolution, of contradictions.

- - - - Tuesday, Nov 17, 2020 - - - -

Computational Logic Seminar: no meeting on Tuesday November 17

The listeners are invited to attend two overlapping zoom events:
http://lp2020.mi-ras.ru/open_lectures/
http://www.math.nsc.ru/conference/malmeet/20/Main.htm

- - - - Wednesday, Nov 18, 2020 - - - -

The New York City Category Theory Seminar
For meeting zoom details email N. Yanofsky.

Speaker: Enrico Ghiorzi, Appalachian State University.
Date and Time: Wednesday November 18, 2020, 7:00 - 8:30 PM., on Zoom.
Title: Internal enriched categories.

Abstract: Internal categories feature a notion of completeness which is remarkably well behaved. For example, the internal adjoint functor theorem requires no solution set condition. Indeed, internal categories are intrinsically small, and thus immune from the size issues commonly afflicting standard category theory. Unfortuntely, they are not quite as expressive as we would like: for example, there is no internal Yoneda lemma. To increase the expressivity of internal category theory, we define a notion of internal enrichment over an internal monoidal category and develop its theory of completeness. The resulting theory unites the good properties of internal categories with the expressivity of enriched category theory, thus providing a powerful framework to work with.

- - - - Thursday, Nov 19, 2020 - - - -

- - - - Friday, Nov 20, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Nov 20, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Philipp Schlicht University of Vienna
The recognisable universe in the presence of measurable cardinals

A set x of ordinals is called recognisable if it is defined, as a singleton, by a formula phi(y) with ordinal parameters that is evaluated in L[y]. The evaluation is always forcing absolute, in contrast to even Sigma_1-formulas with ordinal parameters evaluated in V. Furthermore, this notion is closely related to similar concepts in infinite computation and Hamkins' and Leahy's implicitly definable sets.

It is conjectured that the recognisable universe generated by all recognisable sets is forcing absolute, given sufficient large cardinals. Our goal is thus to determine the recognisable universe in the presence of large cardinals. The new main result, joint with Philip Welch, is a computation of the recognisable universe within the least inner model with infinitely many measurable cardinals.

Next Week in Logic at CUNY:

- - - - Monday, Nov 23, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 23, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Behnam Zolghadr (LMU Munich)

Title: How to Abū Hāšim Meinong

Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.

- - - - Tuesday, Nov 24, 2020 - - - -

- - - - Wednesday, Nov 25, 2020 - - - -

- - - - Thursday, Nov 26, 2020 - - - -

THANKSGIVING RECESS

- - - - Friday, Nov 27, 2020 - - - -

THANKSGIVING RECESS

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Barcelona Set Theory Seminar

Barcelona Logic Seminar

11/15/2020 13:04:08

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

SPEAKER: Monroe Eskew (Vienna)

TITLE: Uncommon systems of embeddings

TIME: November 18 at 16:00 (CET)

PLACE: The Seminar will take place online at the following address:

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://zoom.us/j/91274578083?pwd=SUpDRHBvY0JpMDNXQXJRcFFzeEZvUT09

Error in Zoom link (seminar tomorrow 11 am)

Toronto Set Theory Seminar

11/12/2020 18:09:22

We had a confusion about the zoom link.

We will be using https://zoom.us/j/91274578083?pwd=SUpDRHBvY0JpMDNXQXJRcFFzeEZvUT09

This can also be found in http://www.fields.utoronto.ca/activities/20-21/set-theory-seminar after filling the registration form.

See you tomorrow at 11 am

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Toronto Set Theory Seminar 11 am (local time) tomorrow Friday 13th

Toronto Set Theory Seminar

11/12/2020 11:00:00

Nov 13th
11:00 am

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Ralf Schindler (University of Münster, Germany)

Title: Martin's Maximum^++ implies the P_max axiom (*).

Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

(KGRC) research seminar talk on Thursday, November 12

Kurt Godel Research Center

11/9/2020 11:39:30

Research seminar Kurt Gödel Research Center Thursday, November 12 "Can You Take Komjath's Inaccessible Away?" Hossein Lamei Ramandi (University of Toronto, Ontario, Canada) In this talk we aim to compare Kurepa trees and Aronszajn trees. Moreover, we talk about the affect of large cardinal assumptions on this comparison. Using the the method of walks on ordinals, we will show it is consistent with ZFC that there is a Kurepa tree and every Kurepa tree contains a Souslin subtree, if there is an inaccessible cardinal. This is stronger than Komjath's theorem which asserts the same consistency from two inaccessible cardinals. We will briefly sketch the ideas to prove that our large cardinal assumption is optimal. If time permits, we talk about the comparison of Kurepa trees and Aronszajn trees in the presence of no large cardinal. This is a joint work with Stevo Todorcevic. Time and Place Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you have not received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

This Week in Logic at CUNY

11/8/2020 21:50:45

This Week in Logic at CUNY:

- - - - Monday, Nov 9, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 9, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Eoin Moore (CUNY)
Title: Towards a Justification Logic for FDE

Abstract: In this work-in-progress, I aim to develop a justification logic counterpart to first degree entailment. I produce a logic which is an extension of FDE using justification terms. The results are extended to other paraconsistent logics.

- - - - Tuesday, Nov 10, 2020 - - - -

Computational Logic Seminar

Tuesday, Nov 10, 2-4pm

For meeting zoom details please email sartemov@gmail.com.

Speaker: Daniel Rogozin, Institute for Information Transmission Problems, Russian Academy of Sciences

Title: Categorical and algebraic aspects of the intuitionistic modal logic IEL^-

Abstract: The intuitionistic modal logic IEL^- is a formalisation of intuitionistic beliefs. This logic has been introduced by S. Artemov and T. Protopopescu to provide an intuitionistic view of knowledge agreed with BHK-semantics. One may understand the modal axioms of this logic in computational terms. Such a consideration is of interest for functional programming theory. We construct the modal lambda calculus based Curry-Howard isomorphic to IEL^- and show that this calculus has strong normalisation and Church-Rosser properties. We have a look at categorical semantics of the obtained lambda calculus and see that it is complete with respect to Cartesian closed categories with certain endofunctors.

Algebraically, the IEL^- modality is a prenucleus operator widespread in the theory of locales and point-free topology. We consider predicate extensions of IEL^- (and some similar logics) and provide a sort of Kripke-Joyal semantics for those logics developing several ideas by R. Goldblatt. We show that such intuitionistic predicate modal logics are complete with respect to their cover systems with the Dedekind-MacNeille completion and the representation of Heyting algebras with corresponding operators.

- - - - Wednesday, Nov 11, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Nov 11, 12:00pm

The seminar will take place virtually at 12pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Joel David Hamkins, Oxford University
Continuous models of arithmetic

Ali Enayat had asked whether there is a model of Peano arithmetic (PA) that can be represented as $⟨ Q, \oplus, \otimes ⟩$ , where $\oplus$ and $\otimes$ are continuous functions on the rationals $Q$ . We prove, affirmatively, that indeed every countable model of PA has such a continuous presentation on the rationals. More generally, we investigate the topological spaces that arise as such topological models of arithmetic. The reals $R$ , the reals in any finite dimension $R n$ , the long line and the Cantor space do not, and neither does any Suslin line; many other spaces do; the status of the Baire space is open.

This is joint work with Ali Enayat, myself and Bartosz Wcisło.

- - - - Thursday, Nov 12, 2020 - - - -

- - - - Friday, Nov 13, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Nov 13, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Diana Montoya, University of Vienna
Independence and uncountable cardinals

The classical concept of independence, first introduced by Fichtenholz and Kantorovic has been of interest within the study of combinatorics of the subsets of the real line. In particular the study of the cardinal characteristic $i$ defined as the minimum size of a maximal independent family of subsets of $ω .$ In the first part of the talk, we will review the basic theory, as well as the most important results regarding the independence number. We will also point out our construction of a poset $P$ forcing a maximal independent family of minimal size which turns out to be indestructible after forcing with a countable support iteration of Sacks forcing.

In the second part, we will talk about the generalization (or possible generalizations) of the concept of independence in the generalized Baire spaces, i.e. within the space $κ κ$ when $κ$ is a regular uncountable cardinal and the new challenges this generalization entails. Moreover, for a specific version of generalized independence, we can have an analogous result to the one mentioned in the paragraph above.

This is joint work with Vera Fischer.

Next Week in Logic at CUNY:

- - - - Monday, Nov 16, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 16, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Speaker: Nick Stang

- - - - Tuesday, Nov 17, 2020 - - - -

- - - - Wednesday, Nov 18, 2020 - - - -

- - - - Thursday, Nov 19, 2020 - - - -

- - - - Friday, Nov 20, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Nov 20, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Philipp Schlicht University of Vienna
TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Barcelona Set Theory Seminar

Barcelona Logic Seminar

11/8/2020 15:20:36

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

SPEAKER: Gabriel Goldberg (UC Berkeley)

TITLE: On the uniqueness of elementary embeddings

TIME: 16:00 (CET)

PLACE: The Seminar will take place online at the following address:

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

Seminar at 11 am (Friday 13th) and back to normal following week

Toronto Set Theory Seminar

11/6/2020 15:39:46

Hello all,

I send you the announcement for the following two talks. Notice the unusual time for next week.

Nov 13th
11:00 am

Ralf Schindler (University of Münster, Germany)

Title: Martin's Maximum^++ implies the P_max axiom (*).

Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."

--

Nov 20th
1:30 pm

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Andrea Medini (University of Vienna, Austria)

Title: Topological applications of Wadge theory

Abstract: Wadge theory provides an exhaustive analysis of the
topological complexity of the subsets of a zero-dimensional Polish
space. Fons van Engelen pioneered its applications to topology by
obtaining a classification of the zero-dimensional homogeneous Borel
spaces (recall that a space $X$ is homogeneous if for all $x,y\in X$
there exists a homeomorphism $h:X\longrightarrow X$ such that $h(x)=y$).
As a corollary, he showed that all such spaces (apart from trivial
exceptions) are in fact strongly homogeneous (recall that a space $X$ is
strongly homogeneous if all non-empty clopen subspaces of $X$ are
homeomorphic to each other).

In a joint work with the other members of the “Wadge Brigade” (namely,
Raphaël Carroy and Sandra Müller), we showed that this last result
extends beyond the Borel realm if one assumes AD. We intend to sketch
the proof of this theorem, with a view towards a complete classification
of the zero-dimensional homogeneous spaces under AD.

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Reminder: Toronto Set Theory Seminar Talk Today (in 15 minutes)

Toronto Set Theory Seminar

11/6/2020 13:15:38

Nov 6th 1:30 pm

Zoom Link: https://yorku.zoom.us/j/96087161597

Jonathan Schilhan (University of Vienna, Austria)

Title: Definable maximal families of reals in forcing extensions

Abstract: Many types of combinatorial, algebraic or measure-theoretic
families of reals, such as mad families, Hamel bases or Vitali sets, can
be framed as maximal independent sets in analytic hypergraphs on Polish
spaces. Their existence is guaranteed by the Axiom of Choice, but
low-projective witnesses ($\mathbf{Delta}^1_2$) were only known to exist
in general in models of the form $L[a]$ for a real $a$. Our main result
is that, after a countable support iteration of Sacks forcing or for
example splitting forcing (a less known forcing adding splitting reals)
over L, every analytic hypergraph on a Polish space has a
$\mathbf{\Delta}^1_2$ maximal independent set. As a corollary, this
solves an open problem of Brendle, Fischer and Khomskii by providing a
model with a $\Pi^1_1$ mif (maximal independent family) while the

independence number $\mathfrak{i}$ is bigger than $\aleph_1$.

Thanks for your patience. Due to technical errors, the zoom link was generated really late. See you soon!!!!!!!!!!!

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Logic Seminar 11 Nov 2020 17:00 hrs at NUS by Philipp Schlicht

NUS Logic Seminar

11/5/2020 20:00:42

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 11 Nov 2020, 17:00 hrs Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Speaker: Philipp Schlicht, University of Vienna Title: Structural results about Pi^1_1 and Sigma^1_2 sets URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: Similarities between c.e., Pi^1_1 and Sigma^1_2 sets can be explained by representing Pi^1_1 and Sigma^1_2 sets as c.e. with respect to a transfinite enumeration procedure. This representation is important for classical results about Pi^1_1 and Sigma^1_2 sets, but also for recent results, for instance about randomness at the level of Pi^1_1 by Hjorth and Nies and structural results about Sigma^1_2 sets by Chong, Wu and Yu. In the main result, we calculate the lengths of enumerations. More precisely, we isolate a certain countable ordinal tau and show that the length of an enumeration of a Pi^1_1 or Sigma^1_2 set either equals omega_1 or is below tau, and tau is optimal. This ordinal has many other interesting characterisations. For example, we show that tau is the optimal bound for the countable ranks of wellfounded Sigma^1_2 relations, in analogy with the Kunen-Martin theorem. We will further touch on related structural problems such as calculating Borel ranks of Pi^1_1 and Sigma^1_2 Borel sets. This is joint work with Philip Welch and Merlin Carl.

Matt Foreman: Hilbert's 10th problem for dynamical systems

Boise Logic and Set Theory Seminar

11/4/2020

Please join us for the next meeting of the ELASTIC seminar next Tuesday, November 10, at 3pm. The meeting will take place at https://boisestate.zoom.us/j/98755933038. Speaker: Matt Foreman (UCI) Title: Hilbert's 10th problem for dynamical systems Abstract: A basic problem in smooth dynamics is determining if a system can be distinguished from its inverse, i.e., whether a smooth diffeomorphism T is isomorphic to T^{-1}. We show that this problem is sufficiently general that asking it for particular choices of T is equivalent to the validity of well-known number theoretic conjectures including the Riemann Hypothesis and Goldbach's conjecture. Further one can produce computable diffeomorphisms T such that the question of whether T is isomorphic to T^{-1} is independent of ZFC.

Tagged: Matt Foreman

(KGRC) research seminar talk on Thursday, November 5

Kurt Godel Research Center

11/2/2020 11:16:29

Research seminar Kurt Gödel Research Center Thursday, November 5 "On Continuous Tree-Like Scales and related properties of Internally Approachable structures" Omer Ben-Neria (Hebrew University of Jerusalem, Israel) In his PhD thesis, Luis Pereira isolated and developed several principles of singular cardinals that emerge from Shelah's PCF theory; principles which involve properties of scales, such as the inexistence of continuous Tree-Like scales, and properties of internally approachable structures such as the Approachable Free Subset Property. In the talk, we will discuss these principles and their relations, and present new results from a joint work with Dominik Adolf concerning their consistency and consistency strength. Time and Place Talk at 3:00pm via Zoom: This talk will be given via Zoom. If you haven't received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

Tagged: Omer Ben-Neria

Logic Seminar 4 Nov 2020 17:00 hrs at NUS by Andre Nies

NUS Logic Seminar

11/2/2020 0:34:00

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 4 Nov 2020, 17:00 hrs Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Speaker: Andre Nies, University of Auckland Title: Weak reducibilities on the K-trivial sets URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: Abstract: The K-trivial sets are antirandom in the sense that the initial segment complexity in terms of prefix-free Kolmogorov complexity K grows as slowly as possible. Chaitin introduced this notion in about 1975, and showed that each K-trivial is Turing below the halting set. Shortly after, Solovay proved that a K-trivial set can be noncomputable. In the past two decades, many alternative characterisations of this class have been found: properties such as being low for K, low for Martin-Loef (ML) randomness, and a basis for ML randomness, which state in one way or the other that the set is close to computable. Initially, the class of noncomputable K-trivials appeared to be amorphous. More recently, evidence of an internal structure has been found. Most of these results can be phrased in the language of a mysterious reducibility on the K-trivials which is weaker than Turing's: A is ML-below B if each ML-random computing B also computes A. Bienvenu, Greenberg, Kucera, Nies and Turetsky (JEMS 2016) showed that there an ML-complete K-trivial set. Greenberg, Miller and Nies (JML, 2019) established a dense hierarchy of subclasses of the K-trivials based on fragments of Omega computing the set, and each such subclass is an initial segment for ML. More recent results generalise these approaches using so-called cost functions. They also show that each K-trivial set is ML-equivalent to a c.e. K-trivial. Alternative reducibilities on the K-trivials will be considered near the end of the talk. One of them is related to the extreme lowness notion of strong jump traceability, and appears to be orthogonal to ML-reducibility. Very recent work with Greenberg and Turetsky provides manyfold characterisations in terms of cost functions, and random oracles.

Tagged: Andre Nies

This Week in Logic at CUNY

11/1/2020 21:03:08

This Week in Logic at CUNY:

- - - - Monday, Nov 2, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 2, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Speaker: Heinrich Wansing (Bochum)

Title: A Note on Synonymy in Proof-Theoretic Semantics

Abstract: The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. The paper develops this idea.

- - - - Tuesday, Nov 3, 2020 - - - -

Computational Logic Seminar

Tuesday, Nov 3, 2-4pm

For meeting zoom details please email sartemov@gmail.com.
Speaker: Sergei Artemov, Graduate Center CUNY

Title: Justification Awareness Models

Abstract: We offer a new approach in formal epistemology which overcomes some principal deficiencies of Hintikka-style modal epistemic logic such as logical omniscience, a hidden assumption of the common knowledge of the model, missing evidence representation, etc.

In this project, we pursue two principal ideas: (i) justifications are prime objects of epistemic modeling: knowledge and belief are defined evidence-based concepts; (ii) awareness restrictions are applied to justifications rather than to propositions, which allows for the maintaining of desirable closure properties. The basic resulting structures, Justification Awareness Models, JAMs, naturally include major justification models, Kripke models and, in addition, represent situations with multiple possibly fallible justifications which, in full generality, were previously off the scope of rigorous epistemic modeling.

Attachments area

- - - - Wednesday, Nov 4, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Oct 28, 3:00pm

The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC: Part II

One of the strongest second-order arithmetic systems is full second-order arithmetic Z2Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1nΣn1-choice scheme asserts for every Σ1nΣn1-formula φ(n,X)φ(n,X) that if for every nn, there is a set XX witnessing φ(n,X)φ(n,X), then there is a single set ZZ whose nn-th slice ZnZn is a witness for φ(n,X)φ(n,X). The Σ1nΣn1-dependent choice scheme asserts that every Σ1nΣn1-relation φ(X,Y)φ(X,Y) without terminal nodes has an infinite branch: there is a set ZZ such that φ(Zn,Zn+1)φ(Zn,Zn+1) holds for all nn. The system Z2Z2 proves the Σ12Σ21-choice scheme and the Σ12Σ21-dependent choice scheme. The independence of Π12Π21-choice scheme from Z2Z2 follows by taking a model of Z2Z2 whose sets are the reals of the Feferman-Levy model of ZFZF in which every ℵLnℵnL is countable and ℵLωℵωL is the first uncountable cardinal.

We construct a model of ZF+ACωZF+ACω whose reals give a model of Z2Z2 together with the full choice scheme in which Π12Π21-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.

- - - - Thursday, Nov 5, 2020 - - - -

Philog - Seminar in Logic, Games and Philosophy
On Thursday, November 5 (6:30 PM) we will return to the book by Diaconis and Skyrms . The Zoom talk will be led by Paul Pedersen.
Title: Inverse Inference from Bayes and Laplace to Statistics.

Abstract: You are screening new drugs for a certain disease. Some patients get better by at least a certain amount; some don't. For one new drug, more get better on the drug than on a placebo. How confident should you be of the new drug's effectiveness on the evidence?

A Zoom link will be posted on the webpage https://philog.arthurpaulpedersen.org/

- - - - Friday, Nov 6, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Nov 6, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Ernest Schimmerling, Carnegie Mellon University

Covering at limit cardinals of K

Theorem (Mitchell and Schimmerling, submitted for publication) Assume there is no transitive class model of ZFC with a Woodin cardinal. Let $ν$ be a singular ordinal such that $ν > ω 2$ and $c f (ν) < | ν |$ . Suppose $ν$ is a regular cardinal in K. Then $ν$ is a measurable cardinal in K. Moreover, if $c f (ν) > ω$ , then $o K (ν) \geq c f (ν)$ .

I will say something intuitive and wildly incomplete but not misleading about the meaning of the theorem, how it is proved, and the history of results behind it.

Next Week in Logic at CUNY:

- - - - Monday, Nov 9, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 9, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Eoin Moore (CUNY)
Title: Towards a Justification Logic for FDE

Abstract: In this work-in-progress, I aim to develop a justification logic counterpart to first degree entailment. I produce a logic which is an extension of FDE using justification terms. The results are extended to other paraconsistent logics.

- - - - Tuesday, Nov 10, 2020 - - - -

- - - - Wednesday, Nov 11, 2020 - - - -

- - - - Thursday, Nov 12, 2020 - - - -

- - - - Friday, Nov 13, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Nov 13, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Diana Montoya, University of Vienna
TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Seminar next week

Toronto Set Theory Seminar

10/30/2020 15:54:27

Hello everyone,

Here a list for upcoming talk (I had a typo last week, Ralf Schindle's talk will be the third one in Nov 13th). Links will be provided later.

Nov 6th 1:30 pm

Jonathan Schilhan (University of Vienna, Austria)

Title: Definable maximal families of reals in forcing extensions

Abstract: Many types of combinatorial, algebraic or measure-theoretic
families of reals, such as mad families, Hamel bases or Vitali sets, can
be framed as maximal independent sets in analytic hypergraphs on Polish
spaces. Their existence is guaranteed by the Axiom of Choice, but
low-projective witnesses ($\mathbf{Delta}^1_2$) were only known to exist
in general in models of the form $L[a]$ for a real $a$. Our main result
is that, after a countable support iteration of Sacks forcing or for
example splitting forcing (a less known forcing adding splitting reals)
over L, every analytic hypergraph on a Polish space has a
$\mathbf{\Delta}^1_2$ maximal independent set. As a corollary, this
solves an open problem of Brendle, Fischer and Khomskii by providing a
model with a $\Pi^1_1$ mif (maximal independent family) while the
independence number $\mathfrak{i}$ is bigger than $\aleph_1$.

-----

Nov 13th
11:00 am

Ralf Schindler (University of Münster, Germany)

Title: Martin's Maximum^++ implies the P_max axiom (*).

Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."

------

Nov 20th
1:30 pm

Andrea Medini (University of Vienna, Austria)

Title: Topological applications of Wadge theory

Abstract: Wadge theory provides an exhaustive analysis of the
topological complexity of the subsets of a zero-dimensional Polish
space. Fons van Engelen pioneered its applications to topology by
obtaining a classification of the zero-dimensional homogeneous Borel
spaces (recall that a space $X$ is homogeneous if for all $x,y\in X$
there exists a homeomorphism $h:X\longrightarrow X$ such that $h(x)=y$).
As a corollary, he showed that all such spaces (apart from trivial
exceptions) are in fact strongly homogeneous (recall that a space $X$ is
strongly homogeneous if all non-empty clopen subspaces of $X$ are
homeomorphic to each other).

In a joint work with the other members of the “Wadge Brigade” (namely,
Raphaël Carroy and Sandra Müller), we showed that this last result
extends beyond the Borel realm if one assumes AD. We intend to sketch
the proof of this theorem, with a view towards a complete classification
of the zero-dimensional homogeneous spaces under AD.

-----

Nov 27th
1:30 pm

Sandra Müller (University of Vienna, Austria)

Title: TBA

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Tagged: Jonathan Schilhan

Seminar Today reminder (in half an hour)

Toronto Set Theory Seminar

10/30/2020 13:01:45

In a couple of minutes we will have:

Speaker: Spencer Unger

Time and link: Oct 30, 2020 01:30 PM Eastern Time (US and Canada, i.e. Toronto time)

Join Zoom Meeting
https://us02web.zoom.us/j/89076919828?pwd=Qy8zMGNvNzFrd0toSXQxTThxVkZVUT09

Meeting ID: 890 7691 9828
Passcode: 670870

Title: Reflection properties at successors of singulars.

Abstract: We survey some recent advances in techniques for getting reflection properties at successors of singulars with particular attention to the tree property and stationary reflection

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Tagged: Spencer Unger

Barcelona Set Theory Seminar

Barcelona Logic Seminar

10/30/2020 10:46:25

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

SPEAKER: Giorgio Venturi (University of Campinas)

TITLE: On non-classical models of ZFC

TIME: 416:00 (CET)

PLACE: The Seminar will take place at the following address:

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://philog.arthurpaulpedersen.org/

Tagged: Giorgio Venturi

(KGRC) research seminar talk on Thursday, October 29

Kurt Godel Research Center

10/26/2020 11:51:12

Research seminar Kurt Gödel Research Center Thursday, October 29 "Structural reflection and shrewd cardinals" Philipp Lücke (University of Barcelona, Spain) In my talk, I want to present work dealing with the interplay between Time and Place extensions of the \emph{Downward Löwenheim–Skolem Theorem} to strong logics, large cardinal axioms and set-theoretic reflection principles, focussing on the characterization of large cardinal notions through model- and set-theoretic reflection properties. The work of Bagaria and his collaborators shows that various important objects in the middle and upper reaches of the large cardinal hierarchy can be characterized through principles of \emph{structural reflection}. I will discuss recent results dealing with possible characterizations of notions from the lower part of this hierarchy through the principle $\mathrm{SR}^-$, introduced by Bagaria and Väänänen. These results show that the principle $\mathrm{SR}^-$ is closely connected to the notion of \emph{shrewd cardinals}, introduced by Rathjen in a proof-theoretic context, and embedding characterizations of these cardinals that resembles Magidor's classical characterization of supercompactness. Time and Place This talk will be given via Zoom. If you haven't received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

Tagged: Philipp Lücke

Toronto Set Theory Seminar (First talk of this Term)

Toronto Set Theory Seminar

10/25/2020 11:17:04

Hello Everyone,

The Toronto Set Theory seminar will finally start this semester. The organizer will be organized by two post-docs, ad tradition dictates: David Schrittesser (U-Toronto, cc'ed) and me (Ivan Ongay-Valverde, York).

The first talk of the semester will be given by Spencer Unger who recently moved to Toronto. After that, we will have weekly talks. The second talk will be given by Ralf Schindler from Münste. Here the information:

Speaker: Spencer Unger

Time and link: Oct 30, 2020 01:30 PM Eastern Time (US and Canada, i.e. Toronto time)

Join Zoom Meeting
https://us02web.zoom.us/j/89076919828?pwd=Qy8zMGNvNzFrd0toSXQxTThxVkZVUT09

Meeting ID: 890 7691 9828
Passcode: 670870

Title: Reflection properties at successors of singulars.

Abstract: We survey some recent advances in techniques for getting reflection properties at successors of singulars with particular attention to the tree property and stationary reflection

For the second talk

Speaker: Ralf Schindler

Time and link: Nov 6, 2020 11:00 AM Eastern Time (US and Canada, i.e. Toronto time )

Title: TBA

Abstract: TBA

See you in "a week"

Best

Iván Ongay Valverde (he/his)

My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com

Tagged: Spencer Unger

This Week in Logic at CUNY

10/25/2020 22:11:38

This Week in Logic at CUNY:

- - - - Monday, Oct 26, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, October 26th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Speaker: Lisa Warenski (CUNY)

Title: The Metaphysics of Epistemic Norms

Abstract: A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain. A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory. Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms. But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment? In this paper, I take up these questions for epistemic norms. Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values. Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth.

- - - - Tuesday, Oct 27, 2020 - - - -

Computational Logic Seminar

Tuesday, Oct 27, 2-4pm

For meeting zoom details please email sartemov@gmail.com.

Speaker: John Connor, Graduate Center CUNY

Title: Justification Logics as Internal Languages -- Part 2 of 2

Abstract:

In this talk the justification logic J- is shown to correspond to the internal language of a class of categories. In addition to proving soundness and completeness, we will show that the categorical models and the basic models are in correspondence, and that one can be transformed into the other in a straightforward way.

- - - - Wednesday, Oct 28, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Oct 28, 3:00pm

The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC

One of the strongest second-order arithmetic systems is full second-order arithmetic Z2Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1nΣn1-choice scheme asserts for every Σ1nΣn1-formula φ(n,X)φ(n,X) that if for every nn, there is a set XX witnessing φ(n,X)φ(n,X), then there is a single set ZZ whose nn-th slice ZnZn is a witness for φ(n,X)φ(n,X). The Σ1nΣn1-dependent choice scheme asserts that every Σ1nΣn1-relation φ(X,Y)φ(X,Y) without terminal nodes has an infinite branch: there is a set ZZ such that φ(Zn,Zn+1)φ(Zn,Zn+1) holds for all nn. The system Z2Z2 proves the Σ12Σ21-choice scheme and the Σ12Σ21-dependent choice scheme. The independence of Π12Π21-choice scheme from Z2Z2 follows by taking a model of Z2Z2 whose sets are the reals of the Feferman-Levy model of ZFZF in which every ℵLnℵnL is countable and ℵLωℵωL is the first uncountable cardinal.

We construct a model of ZF+ACωZF+ACω whose reals give a model of Z2Z2 together with the full choice scheme in which Π12Π21-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.

- - - - Thursday, Oct 29, 2020 - - - -

Seminar in Logic, Games and Philosophy

Zoom seminar, Thursday October 29 at 6:30 PM

Cailin O'Connor, UC Irvine

Title: Measuring Conventionality

Abstract: Standard accounts of convention include notions of arbitrariness. But many have conceived of conventionality as an all or nothing affair. In this paper, I develop a framework for thinking of conventions as coming in degrees of arbitrariness. In doing so, I introduce an information theoretic measure intended to capture the degree to which a solution to a certain social problem could have been otherwise. As the paper argues, this framework can help improve explanation aimed at the cultural evolution of social traits. Good evolutionary explanations recognize that most functional traits are also conventional, at least to some degree, and vice versa.

A zoom link will be posted on Wednesday at

- - - - Friday, Oct 30, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 30, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Benedikt Löwe, University of Hamburg
TBA

Workshop on Substructural Logics, Hierarchies Thereof, and Solutions to the Liar

The Logic and Metaphysics Workshop and the Saul Kripke Center are hosting a day of talks on substructural Logics, hierarchies thereof, and solutions to the Liar on Friday, October 30, 2020. The schedule, NY time, will be as follows (abstracts can be accessed here):

10.00. Strict/Tolerant and Tolerant/Strict Logics, Melvin Fitting, CUNY.
11.40. Expressibility and the (Un)paradoxicality Paradoxes, Will Nava, NYU.
1.20. Lunch Break.
2.00. What is Meta-inferential Validity?, Chris Scambler, NYU.
3.40. Supervaluations and the Strict-Tolerant Hierarchy, Brian Porter, CUNY.
5.20. End (virtual gathering).

Talks will be on Zoom, and are open to all interested. A link will be sent out on the mailing lists of the Logic and Metaphysics Workshop and the Saul Kripke Center the day before. People not on either of those lists who want to receive the link should email Graham Priest (priest DOT graham AT gmail DOT com). PLEASE FEEL FREE TO PASS ON THIS ANNOUNCEMENT.

Next Week in Logic at CUNY:

- - - - Monday, Nov 2, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 2, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Speaker: Lisa Warenski (CUNY).
Title: The Metaphysics of Epistemic Norms

Abstract: A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain. A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory. Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms. But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment? In this paper, I take up these questions for epistemic norms. Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values. Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth.

- - - - Tuesday, Nov 3, 2020 - - - -

- - - - Wednesday, Nov 4, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Oct 28, 3:00pm

The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC: Part II

One of the strongest second-order arithmetic systems is full second-order arithmetic $Z 2$ which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment $Z 2$ with choice principles such as the choice scheme and the dependent choice scheme. The $Σ 1 n$ -choice scheme asserts for every $Σ 1 n$ -formula $φ (n, X)$ that if for every $n$ , there is a set $X$ witnessing $φ (n, X)$ , then there is a single set $Z$ whose $n$ -th slice $Z n$ is a witness for $φ (n, X)$ . The $Σ 1 n$ -dependent choice scheme asserts that every $Σ 1 n$ -relation $φ (X, Y)$ without terminal nodes has an infinite branch: there is a set $Z$ such that $φ (Z n, Z n + 1)$ holds for all $n$ . The system $Z 2$ proves the $Σ 12$ -choice scheme and the $Σ 12$ -dependent choice scheme. The independence of $Π 12$ -choice scheme from $Z 2$ follows by taking a model of $Z 2$ whose sets are the reals of the Feferman-Levy model of $Z F$ in which every $ℵ L n$ is countable and $ℵ L ω$ is the first uncountable cardinal.

We construct a model of $Z F + A C ω$ whose reals give a model of $Z 2$ together with the full choice scheme in which $Π 12$ -dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.

- - - - Thursday, Nov 5, 2020 - - - -

- - - - Friday, Nov 6, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 30, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Ernest Schimmerling, Carnegie Mellon University
TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Barcelona Set Theory Seminar

Barcelona Logic Seminar

10/25/2020 10:26:58

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

The Seminar will take place at the following address:

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

(KGRC) research seminar talk on Thursday, October 22

Kurt Godel Research Center

10/19/2020 10:55:49

Research seminar Kurt Gödel Research Center Thursday, October 22 "Tree forcings, sharps and absoluteness" Philipp Schlicht (KGRC) In joint results with Fabiana Castiblanco from 2018, we showed that several classical tree forcings preserve sharps for reals and levels of projective determinacy, and studied their impact on definable equivalence relations (in particular, the question whether they add equivalence classes to thin projective equivalence relations). I will discuss these results and natural open problems on tree forcings and absoluteness that arise from them. Time and Place This talk will be given via Zoom. If you haven't received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

Tagged: Philipp Schlicht

Barcelona Set Theory Seminar

Barcelona Logic Seminar

10/19/2020 9:21:05

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

The Seminar will take place at the following address:

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Barcelona Set Theory Seminar

Barcelona Logic Seminar

10/19/2020 9:21:23

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

The Seminar will take place at the following address:

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

This Week in Logic at CUNY

10/18/2020 22:15:53

This Week in Logic at CUNY:

- - - - Monday, Oct 19, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, October 19th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Michael Glanzberg (Rutgers)

Title: Models, Model Theory, and Modeling

Abstract: In this paper, I shall return to the relations between logic and semantics of natural language. My main goal is to advance a proposal about what that relation is. Logic as used in the study of natural language—an empirical discipline—functions much like specific kinds of scientific models. Particularly, I shall suggest, logics can function like analogical models. More provocatively, I shall also suggest they can function like model organisms often do in the biological sciences, providing a kind of controlled environment for observations. My focus here will be on a wide family of logics that are based on model theory, so in the end, these claims apply equally to model theory itself. Along the way towards arguing for my thesis about models in science, I shall also try to clarify the role of model theory in logic. At least, I shall suggest, it can play distinct roles in each domain. It can offer something like scientific models when it comes to empirical applications, while at the same time furthering conceptual analysis of a basic notion of logic.

- - - - Tuesday, Oct 20, 2020 - - - -

Computational Logic Seminar

Tuesday, Oct 20, 2-4pm

For meeting zoom details please email sartemov@gmail.com.

Speakers: Pavel Naumov (King's College, Pennsylvania) and Rui-Jie Yew (Scripps College, California)

Title: An Epistemic Logic of Desire

Abstract: We say that an agent desires a condition phi if (1) the agent knows neither that phi is true nor that phi is false (2) among all indistinguishable worlds, she prefers those in which phi is true. In this talk, I will propose a sound and complete logical system that describes the interplay between the desire and the knowledge modalities in the multiagent setting.

- - - - Wednesday, Oct 21, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Oct 21, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Roman Kossak, CUNY
Types, gaps, and pairs of models of PA, Part III

The talk will be a survey of results on first-order theories of pairs (N,M), where M is a model of PA and N is its elementary extension, under various assumptions on the models and on the type of extension. In particular, I will discuss in detail the results on countable recursively saturated models and their cofinal submodels from a joint paper with Jim Schmerl.

The New York City Category Theory Seminar
Speaker: Andrei V. Rodin, Saint Petersburg State University.
Date and Time: Wednesday October 21, 2020, 7:00 - 8:30 PM., on Zoom.

For meeting zoom details email N. Yanofsky.
TBA

- - - - Thursday, Oct 22, 2020 - - - -

- - - - Friday, Oct 23, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 23, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Gabriel Goldberg, University of Berkeley

Ultrapowers and the approximation property

Countably complete ultrafilters are the combinatorial manifestation of strong large cardinal axioms, but many of their basic properties are undecidable no matter the large cardinal axioms one is willing to adopt. The Ultrapower Axiom (UA) is a set theoretic principle that permits the development of a much clearer picture of countably complete ultrafilters and, consequently, the large cardinals from which they derive. It is not known whether UA is (relatively) consistent with very large cardinals, but assuming there is a canonical inner model with a supercompact cardinal, the answer should be yes: this inner model should satisfy UA and yet inherit all large cardinals present in the universe of sets. The predicted resemblance between the large cardinal structure of this model and that of the universe itself is so extreme as to suggest that certain consequences of UA must in fact be provable outright from large cardinal axioms. While the inner model theory of supercompact cardinals remains a major open problem, this talk will describe a technique that already permits a number of consequences of UA to be replicated from large cardinals alone. Still, the technique rests on the existence of inner models that absorb large cardinals, but instead of building canonical inner models, one takes ultrapowers.

Next Week in Logic at CUNY:

- - - - Monday, Oct 26, 2020 - - - -

- - - - Tuesday, Oct 27, 2020 - - - -

- - - - Wednesday, Oct 28, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Oct 28, 2:00pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC

One of the strongest second-order arithmetic systems is full second-order arithmetic $Z 2$ which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment $Z 2$ with choice principles such as the choice scheme and the dependent choice scheme. The $Σ 1 n$ -choice scheme asserts for every $Σ 1 n$ -formula $φ (n, X)$ that if for every $n$ , there is a set $X$ witnessing $φ (n, X)$ , then there is a single set $Z$ whose $n$ -th slice $Z n$ is a witness for $φ (n, X)$ . The $Σ 1 n$ -dependent choice scheme asserts that every $Σ 1 n$ -relation $φ (X, Y)$ without terminal nodes has an infinite branch: there is a set $Z$ such that $φ (Z n, Z n + 1)$ holds for all $n$ . The system $Z 2$ proves the $Σ 12$ -choice scheme and the $Σ 12$ -dependent choice scheme. The independence of $Π 12$ -choice scheme from $Z 2$ follows by taking a model of $Z 2$ whose sets are the reals of the Feferman-Levy model of $Z F$ in which every $ℵ L n$ is countable and $ℵ L ω$ is the first uncountable cardinal.

We construct a model of $Z F + A C ω$ whose reals give a model of $Z 2$ together with the full choice scheme in which $Π 12$ -dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.

Tuesday, Oct 6, 2-4pm

For meeting zoom details please email sartemov@gmail.com.

Speaker: Sergei Artemov, Graduate Center CUNY

Title: On aggregating probabilistic evidence

Abstract: Imagine a database—a set of propositions Γ = {F1, . . . , Fn} with some kind of probability estimates and let a proposition X logically follow from Γ . What is the best justified lower bound of the probability of X? The traditional approach, e.g. within Adams’ probability logic, computes the numeric lower bound for X corresponding to the worst-case scenario. We suggest a more flexible parameterized approach by assuming probability events u1, u2, . . . , un that support Γ and calculating aggregated evidence e(u1, u2, . . . , un) for X. The probability of e provides a tight lower bound for any, not only a worst-case, situation. The problem is formalized in a version of justification logic and the conclusions are supported by corresponding completeness theorems. This approach can handle conflicting and inconsistent data and allows the gathering both positive and negative evidence for the same proposition.

- - - - Wednesday, Oct 14, 2020 - - - -

The New York City Category Theory Seminar

Speaker: Jonathon Funk, Queensborough CUNY.
Date and Time: Wednesday October 14, 2020, 6:00 - 7:30PM (NOTICE DIFFERENT TIME) on Zoom.

For meeting zoom details email N. Yanofsky.
Title: Pseudogroup Torsors.

Abstract: We use sheaf theory to analyze the topos of etale actions on the germ groupoid of a pseudogroup in the sense that we present a site for this topos, which we call the classifying topos of the pseudogroup. Our analysis carries us further into how pseudogroup morphisms and geometric morphisms are related. Ultimately, we shall see that the classifying topos classifies what we call a pseudogroup torsor. In hindsight, we see that pseudogroups form a bicategory of `flat' bimodules.

Joint work with Pieter Hofstra.

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Oct 14, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Roman Kossak, CUNY
Types, gaps, and pairs of models of PA, Part II

The talk will be a survey of results on first-order theories of pairs (N,M), where M is a model of PA and N is its elementary extension, under various assumptions on the models and on the type of extension. In particular, I will discuss in detail the results on countable recursively saturated models and their cofinal submodels from a joint paper with Jim Schmerl.

- - - - Thursday, Oct 15, 2020 - - - -

- - - - Friday, Oct 16, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 16, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Richard Matthews, University of Leeds

Taking Reinhardt's Power Away

Many large cardinals can be defined through elementary embeddings from the set-theoretic universe to some inner model, with the guiding principle being that the closer the inner model is to the universe the stronger the resulting theory. Under ZFC, the Kunen Inconsistency places a hard limit on how close this can be. One is then naturally led to the question of what theory is necessary to derive this inconsistency with the primary focus having historically been embeddings in ZF without Choice.

In this talk we take a different approach to weakening the required theory, which is to study elementary embeddings from the universe into itself in ZFC without Power Set. We shall see that I1, one of the largest large cardinal axioms not known to be inconsistent with ZFC, gives an upper bound to the naive version of this question. However, under reasonable assumptions, we can reobtain this inconsistency in our weaker theory.

Next Week in Logic at CUNY:

- - - - Monday, Oct 19, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, October 19th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu

Michael Glanzberg (Rutgers)

Title: Models, Model Theory, and Modeling

Abstract: In this paper, I shall return to the relations between logic and semantics of natural language. My main goal is to advance a proposal about what that relation is. Logic as used in the study of natural language—an empirical discipline—functions much like specific kinds of scientific models. Particularly, I shall suggest, logics can function like analogical models. More provocatively, I shall also suggest they can function like model organisms often do in the biological sciences, providing a kind of controlled environment for observations. My focus here will be on a wide family of logics that are based on model theory, so in the end, these claims apply equally to model theory itself. Along the way towards arguing for my thesis about models in science, I shall also try to clarify the role of model theory in logic. At least, I shall suggest, it can play distinct roles in each domain. It can offer something like scientific models when it comes to empirical applications, while at the same time furthering conceptual analysis of a basic notion of logic.

- - - - Tuesday, Oct 20, 2020 - - - -

- - - - Wednesday, Oct 21, 2020 - - - -

The New York City Category Theory Seminar
Speaker: Andrei V. Rodin, Saint Petersburg State University.
Date and Time: Wednesday October 21, 2020, 7:00 - 8:30 PM., on Zoom.

For meeting zoom details email N. Yanofsky.
TBA

- - - - Thursday, Oct 22, 2020 - - - -

- - - - Friday, Oct 23, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 23, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Gabriel Goldberg, University of Berkeley
TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

10/11/2020 11:45:39

Dear all, Well, no Wednesday seminar next week, no seminars until further notice. Best, David

Barcelona Set Theory Seminar

Barcelona Logic Seminar

10/11/2020 3:31:18

Dear All,

Please find attached the announcement of the next session of the Barcelona Set Theory Seminar. Feel free to distribute it.

The Seminar will take place at the following address:

Best regards,

Joan

P.S.: If you do not wish to receive any more announcements, please send an email to bagaria@ub.edu with the text “Unsubscribe”.

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

https://eu.bbcollab.com/guest/2bd01807690a4ae39a8f102e19911a31

Logic Seminar 14 Oct 2020 17:00 hrs at NUS by Tran Chieu-Minh (University of Notre Dame)

NUS Logic Seminar

10/9/2020 1:12:36

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 14 Oct 2020, 17:00 hrs Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Speaker: Tran Chieu-Minh Title: Incidence counting and trichotomy in o-minimal structures URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: Zarankiewicz's problem in graph theory asks to determine the largest possible number of edges |E| in a bipartite graph G = (V_1, V_2; E) with the parts V_1 and V_2 containing n_1 and n_2 vertices, respectively, and such that G contains no complete bipartite subgraphs on k vertices. Graphs definable in o-minimal (or more generally distal structures) enjoy stronger bounds than general graphs, providing an abstract setting for the Szemeredi-Trotter theorem and related incidence bounds. We obtain almost optimal upper and lower bounds for hypergraphs definable in locally modular o-minimal structures, along with some applications to incidence counting (e.g. the number of incidences between points and boxes with axis parallel sides on the plane whose incidence graph is K_{k,k}-free is almost linear). We explain how the exponent appearing in these bounds is tightly connected to the trichotomy principle in o-minimal structures. Joint work with Abdul Basit, Artem Chernikov, Sergei Starchenko and Terence Tao.

Link to the Barcelona Set Theory Seminar

Barcelona Logic Seminar

10/6/2020 3:45:39

Dear All,

Just to let you know that the link to the Barcelona Set Theory Seminar is the following:

The first session of the Seminar will be tomorrow, Wednesday 7, at 16.00 (CEST). You may use the same link for all the following sessions.

See you there!

Joan

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

Clovis Hamel: An introduction to Cp-theory and Grothendieck spaces

Toronto Set Theory Seminar

2/7/2021

Place: Fields Institute (Room 210) Date: October 11, 2019 (13:30-15:00) Speaker: Clovis Hamel Title: An introduction to Cp-theory and Grothendieck spaces Abstract: This is joint work with Prof. Frank Tall. An old theorem of Grothendieck states that countably compact subspaces of Cp(X) have compact closure whenever X is countably compact. We shall survey some basic results in Cp-theory and then focus on Grothendieck spaces, i.e. those for which the conclusion of Grothendieck theorem holds. Following Arhangel'skiĭ, we shall introduce the Lindelöf Σ-spaces, which belong to a wide class of well-behaved spaces, and prove that they are Grothendieck. We will show a compactness criterion for Fréchet-Urysohn Grothendieck spaces involving exchanging (ultra)limits which is similar to the classical Ptak's lemma. In a later occasion, we shall show the relevance of this results in Model Theory, e.g. the definability of pathological Banach spaces in various continuous logics.

Tagged: Clovis Hamel

(KGRC) research seminar talk on Thursday, October 8

Kurt Godel Research Center

10/5/2020 10:32:50

The KGRC welcomes as guests: The visit by Jerzy Kąkol (host: Damian Sobota) had to be canceled due to COVID travel restrictions. The visit by Colin Jahel (host: Noé de Rancourt), too, had to be canceled due to COVID travel restrictions; the talk will be given via Zoom (see below). Ziemowit Kostana (host: Noé de Rancourt) will visit from October 15 to October 20, 2020 and give a talk (talk to be announced later). * * * Research seminar Kurt Gödel Research Center Thursday, October 8 "Actions of automorphism groups of Fraïssé limits on the space of linear orderings" Colin Jahel (Claude Bernard University Lyon 1, France) In 2005, Kechris, Pestov and Todorčević exhibited a correspondence between combinatorial properties of structures and dynamical properties of their automorphism groups. In 2012, Angel, Kechris and Lyons used this correspondence to show the unique ergodicity of all the actions of some groups. In this talk, I will give an overview of the aforementioned results and discuss recent work generalizing results of Angel, Kechris and Lyons. Time and Place Talk at 3:00pm This talk will be given via Zoom. If you haven't received the meeting link by the day before the talk, please contact richard.springer@univie.ac.at!

This Week in Logic at CUNY

10/4/2020 21:34:47

This Week in Logic at CUNY:

- - - - Monday, Oct 5, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, October 5th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Speaker: Oliver Marshall (UNAM)
Title: Mathematical Information Content

Abstract: Alonzo Church formulated several logistic theories of propositions based on three alternative criteria of identity (1949, 1954, 1989, 1993). The most coarse grained of these criteria is Alternative (2), according to which two propositions are identical iff the sentences that express them are necessarily materially equivalent. Alternative (1) is more discerning. According to Alternative (1), two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms and λ-conversion. Church said that he intended this to limn a notion of proposition closely related to Frege’s notion of gedanke, but added that it will not be sufficiently discerning if propositions in the sense of Alternative (1) are taken as objects of assertion and belief (1993). Alternative (0), the most discerning criterion, says that two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms. I argue that Alternative (1) does indeed provide insight into one of the topics that concerned Frege (1884) – namely, abstraction. Then I discuss various counterexamples to Church’s criteria (including one due to Paul Bernays, 1961). I close by proposing a criterion of identity for mathematical information content based on the various examples under discussion.

- - - - Tuesday, Oct 6, 2020 - - - -

Computational Logic Seminar

Tuesday, Oct 6, 2-4pm

For meeting zoom details please email sartemov@gmail.com.

Speaker: John Connor, Graduate Center CUNY
Title: Justification Logics as Internal Languages -- Part 1 of 2

Abstract:
This is the first of two talks in which I answer the question (in the affirmative) of whether the justification logic J is the internal language of a class of categories. In this first talk we will discuss the methods by which a logic may be interpreted in a category, and the properties such interpretations may have. Concrete examples will include propositional intuitionistic logic as the internal language of bi-Cartesian closed categories. Some aspects of the interpretation of higher logics in topoi will also be discussed. Previous knowledge of category theory is not assumed.

The talk concludes with a discussion of the difficulties inherent in the interpretation of justification logics. In the next talk, a class of categories is presented with respect to which the justification logic J is sound and complete in a weak sense.

- - - - Wednesday, Oct 7, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Oct 7, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Roman Kossak, CUNY
Types, gaps, and pairs of models of PA

- - - - Thursday, Oct 8, 2020 - - - -

- - - - Friday, Oct 9, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 9, 11am

The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Heike Mildenberger, Albert-Ludwigs-Universität Freiburg
Forcing with variants of Miller trees

Guzmán and Kalajdzievski introduced a variant of Miller forcing $P (F)$ that diagonalises a given filter $F$ over $ω$ and has Axiom A. We investigate the effect of $P (F)$ for particularly chosen Canjar filters $F$ . This is joint work with Christian Bräuninger.

Next Week in Logic at CUNY:

- - - - Monday, Oct 12, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, October 12th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Brian Cross Porter (CUNY).
Title: A Metainferential Hierachy of Validity Curry Paradoxes

Abstract: The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of metaninferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox.

- - - - Tuesday, Oct 13, 2020 - - - -

- - - - Wednesday, Oct 14, 2020 - - - -

The New York City Category Theory Seminar

Speaker: Jonathon Funk, Queensborough CUNY.
Date and Time: Wednesday October 14, 2020, 6:00 - 7:30PM (NOTICE DIFFERENT TIME) on Zoom.

For meeting zoom details email N. Yanofsky.
Title: Pseudogroup Torsors.

Abstract: We use sheaf theory to analyze the topos of etale actions on the germ groupoid of a pseudogroup in the sense that we present a site for this topos, which we call the classifying topos of the pseudogroup. Our analysis carries us further into how pseudogroup morphisms and geometric morphisms are related. Ultimately, we shall see that the classifying topos classifies what we call a pseudogroup torsor. In hindsight, we see that pseudogroups form a bicategory of `flat' bimodules.

Joint work with Pieter Hofstra.

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Oct 14, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Roman Kossak, CUNY
Types, gaps, and pairs of models of PA

- - - - Thursday, Oct 15, 2020 - - - -

- - - - Friday, Oct 16, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 16, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Richard Matthews, University of Leeds
TBA

- - - - Other Logic News - - - -

Ad hoc logic workshop

There is some interesting work going on in NYC at the moment on substructural logics, hierarchies thereof, and solutions to the liar. So we're scheduling an ad hoc workshop on these matters (by Zoom), with talks by Mel Fitting, Will Nava, Brian Porter, and Chris Scambler. It will be on Friday 30th October. The aim will be to have two papers in the morning, and two in the afternoon. Full details will be sent round in due course. This is just an early warning to make a note of the date if you are interested. - Graham Priest

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

10/4/2020 15:52:49

Dear all, Still no seminar the coming Wednesday, October 7th. Unless there is a major the development, I expect the seminar to resume on Wednesday October 14th. (The originally scheduled off-site meeting got cancelled.) Best, David

Invitation to Logic Seminar 7 Oct 2020 17:00 hrs at NUS by Wu Guohua

NUS Logic Seminar

10/2/2020 9:28:07

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 7 October 2020, 17:00 hrs Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Speaker: Wu Guohua Title: Splittings URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: I will present a survey of splittings in sets and in degrees. Downey-Stob's long paper in 1993 provides a comprehensive and updated survey. In this talk, I first recall some classical theorems on this topic, both ideas and techniques, and following this, I will present some results along this line being done in the last few years.

Tagged: Wu Guohua

Barcelona Set Theory seminar

Barcelona Set Theory Seminar

10/1/2020 10:59:55

Dear Colleague,

Next week we will start our online Barcelona Set Theory seminar, which will meet every Wednesday at 4:00 (CEST). Please find attached the announcement of the next session. Feel free to distribute it.

If you wish to attend, please send an email to bagaria@ub.edu and we’ll send you the link.

Best regards,

Joan

Joan Bagaria

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

This Week in Logic at CUNY

9/27/2020 21:59:56

This Week in Logic at CUNY:

- - - - Monday, Sep 21, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, September 21st, 4.15-6.15 (NY time)

For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Yale Weiss (CUNY)
Title: Arithmetical Semantics for Non-Classical Logic

Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.

- - - - Tuesday, Sep 22, 2020 - - - -

Computational Logic Seminar
Time 2:00 - 4:00 PM Tuesday, September 22, 2020
Please send me a request for a link to this talk: (unless you are registered or have already sent me a request for the whole semester).
Speaker: Hirohiko Kushida, Graduate Center, City University of New York
Title: Reduction of Modal Logic and Realization in Justification Logic

Abstract: In this paper, we first offer basic results on modal logic: (1) a wide range of modal systems can be syntactically reduced to the modal logic K in terms of theoremhood and (2) we can restrict the forms of modal axioms without changing their deductive power in those range of modal logics. Then, based on these results, we offer a new, simple, uniform and modular proof-theoretical proof of the realization of a wide range of modal logics with possible combinations of modal axioms T, D, 4, 5 including S5 in Justification Logic. We do not use a generalization of sequent calculus such as hypersequent and nested sequent calculi. We just utilize the standard cut-free sequent calculus for K and then we show, in the realized proof in Justification Logic (corresponding to K), how to recover the realizations of the modal axioms by rewriting terms in the proof.

- - - - Wednesday, Sep 23, 2020 - - - -

- - - - Thursday, Sep 24, 2020 - - - -

Seminar in Philosophical Logic
Thursday, Sep 24, 6:30 PM.
(Zoom link upon request RParikh@gc.cuny.edu; will be sent automatically to seminar members)
Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY
Coherent Judgment: Previsions and Forecasts

Abstract. This talk is to continue critical discussion of Persi Diaconis and Brian Skyrms' book chapter, "Judgment," from their Ten Great Ideas about Chance (Princeton University Press, 2018). Specifically, I will cover two variations on coherence advanced by de Finetti to justify his theory of personal probability, each cast in game-theoretic terms — one based on previsions, the other based on forecasting. I will show how his ideas extend both conceptually and mathematically to subsequent developments due to Savage, Anscombe & Aumann, and others. While the talk is to be self-contained, an excellent reference for broader discussion is Peter Fishburn's "Utility and Subjective Probability: Contemporary Theories," International Encyclopedia of the Social & Behavioral Sciences, 2001: 16113-16121.

- - - - Friday, Sep 25, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Sep 25, 11am

The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Ralf Schindler, University of Münster
Martin's Maximum^++ implies the P_max axiom (*)

Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.

Next Week in Logic at CUNY:

- - - - Monday, Sep 28, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, September 29st, 4.15-6.15 (NY time)

For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Daniel Hoek (Virginia Tech)
Title: Coin flips, Spinning Tops and the Continuum Hypothesis

Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).

- - - - Tuesday, Sep 29, 2020 - - - -

- - - - Wednesday, Sep 30, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Sep 30, 2:00pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Leszek Kołodziejczyk University of Warsaw
Ramsey's Theorem over RCA∗0RCA0∗: Part II

Abstract: The usual base theory used in reverse mathematics, RCA0RCA0, is the fragment of second-order arithmetic axiomatized by Δ01Δ10 comprehension and Σ01Σ10 induction. The weaker base theory RCA∗0RCA0∗ is obtained by replacing Σ01Σ10 induction with Δ01Δ10 induction (and adding the well-known axiom expexp in order to ensure totality of the exponential function). In first-order terms, RCA0RCA0 is conservative over IΣ1IΣ1 and RCA∗0RCA0∗ is conservative over BΣ1+expBΣ1+exp.

Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0RCA0∗.

Given standard natural numbers n,k≥2n,k≥2, let RTnkRTkn stand for Ramsey's Theorem for kk-colourings of nn-tuples. We first show that assuming the failure of Σ01Σ10 induction, RTnkRTkn is equivalent to its own relativization to an arbitrary Σ01Σ10-definable cut. Using this, we give a complete axiomatization of the first-order consequences of RCA∗0+RTnkRCA0∗+RTkn for n≥3n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of RT2kRTk2. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of RT22RT22 over the traditional base theory RCA0RCA0.

In the first part of the talk, we concentrated on Ramsey's Theorem for nn-tuples where n≥3n≥3. In this second part, the focus will be on RT22RT22.

The New York City Category Theory Seminar
Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html

Speaker: David Ellerman, University of Ljubljana.
Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.

Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps.
Paper: Available here http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf

- - - - Thursday, Oct 1, 2020 - - - -

- - - - Friday, Oct 2, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 2, 11am

The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

David Aspero, University of East Anglia

Martin’s Maximum^++ implies the P_max axiom (*) (Part 2)

This will be a sequel to Ralf Schindler’s talk on 9/25. My plan is to give a reasonably detailed account of the proof of the result in the title.

Next Week in Logic at CUNY:

- - - - Monday, Oct 5, 2020 - - - -

- - - - Tuesday, Oct 6, 2020 - - - -

- - - - Wednesday, Oct 7, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Oct 7, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Roman Kossak, CUNY
Types, gaps, and pairs of models of PA

- - - - Thursday, Oct 8, 2020 - - - -

- - - - Friday, Oct 9, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 9, 11am

The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Heike Mildenberger, Albert-Ludwigs-Universität Freiburg
TBA

- - - - Other Logic News - - - -

Ad hoc logic workshop

There is some interesting work going on in NYC at the moment on substructural logics, hierarchies thereof, and solutions to the liar. So we're scheduling an ad hoc workshop on these matters (by Zoom), with talks by Mel Fitting, Will Nava, Brian Porter, and Chris Scambler. It will be on Friday 30th October. The aim will be to have two papers in the morning, and two in the afternoon. Full details will be sent round in due course. This is just an early warning to make a note of the date if you are interested. - Graham Priest

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

9/27/2020 8:14:24

Dear all, As the general epidemiological situation remains uncertain, there will be no seminar next week, Wednesday October 30th. I expect the seminar to resume during October. (Probably no seminar on October 14th -- our Institute holds an off-site meeting.) Best, David

Logic Seminar 30 Sept 2020 17:00 hrs by Vasco Brattka (Universitaet der Bundeswehr Muenchen)

NUS Logic Seminar

9/23/2020 23:49:10

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 30 September 2020, 17:00 hrs Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Speaker: Vasco Brattka Title: The Discontinuity Problem URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract We discuss the question whether there is a weakest unsolvable mathematical problem. In recent years the Weihrauch lattice has been established as a suitable computability theoretic framework to analyze the uniform computational content of problems from many different fields of mathematics. Here we answer a question by Schroeder, whether there is a weakest discontinuous problem with respect to the continuous version of Weihrauch reducibility. We introduce the discontinuity problem, and we show that it is reducible exactly to the effectively discontinuous problems, defined in a suitable way. However, in which sense this answers Schroeder's question sensitively depends on the axiomatic framework that is chosen and it is a positive answer if we work in Zermelo- Fraenkel set theory with dependent choice and the axiom of determinacy. On the other hand, using the axiom of choice, one can construct problems which are discontinuous, but not effectively so. Hence, the exact structure of the ``bottom'' of the Weihrauch lattice sensitively depends on the axiomatic setting that we choose. We prove our result using Wadge games for mathematical problems and while the existence of a winning strategy for player II characterizes continuity of the problem (as already shown by Nobrega and Pauly), the existence of a winning strategy for player I characterizes effective discontinuity of the problem. We also provide further insights into the algebraic nature of the discontinuity problem. For one we show that the parallelization of the discontinuity problem is exactly the non-computability problem that was studied before. One the other hand, we introduce a new algebraic operation in the Weihrauch lattice that we call summation and which is the dual operation to parallelization. While parallelization can be seen as an analogue of the bang operator in linear logic, summation can be seen as an analogue of the question mark operator. It turns out that the discontinuity problem can be obtained as summation of a number of well-known problems in the Weihrauch lattice, such as the (lesser) limited problem of omniscience and variants thereof. More generally, we study the action of the monoid formed by parallelization and summation on the Weihrauch lattice, and we prove that this action can lead to at most five different Weihrauch degrees, which (in the maximal case) are always organized in a pentagon. We show that the discontinuity problem appears as the bottom of several natural such pentagons. This leads to further interesting characterizations of the discontinuity problem.

Tagged: Vasco Brattka

UPDATE - This Week in Logic at CUNY

This Week in Logic at CUNY

9/20/2020 22:00:19

Added the talk on Tuesday Sep 22 in the Computational Logic Seminar

-Jonas

This Week in Logic at CUNY:

- - - - Monday, Sep 21, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, September 21st, 4.15-6.15 (NY time)

For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Yale Weiss (CUNY)
Title: Arithmetical Semantics for Non-Classical Logic

Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.

- - - - Tuesday, Sep 22, 2020 - - - -

Computational Logic Seminar
Time 2:00 - 4:00 PM Tuesday, September 22, 2020
Please send me a request for a link to this talk: (unless you are registered or have already sent me a request for the whole semester).
Speaker: Hirohiko Kushida, Graduate Center, City University of New York
Title: Reduction of Modal Logic and Realization in Justification Logic

Abstract: In this paper, we first offer basic results on modal logic: (1) a wide range of modal systems can be syntactically reduced to the modal logic K in terms of theoremhood and (2) we can restrict the forms of modal axioms without changing their deductive power in those range of modal logics. Then, based on these results, we offer a new, simple, uniform and modular proof-theoretical proof of the realization of a wide range of modal logics with possible combinations of modal axioms T, D, 4, 5 including S5 in Justification Logic. We do not use a generalization of sequent calculus such as hypersequent and nested sequent calculi. We just utilize the standard cut-free sequent calculus for K and then we show, in the realized proof in Justification Logic (corresponding to K), how to recover the realizations of the modal axioms by rewriting terms in the proof.

- - - - Wednesday, Sep 23, 2020 - - - -

- - - - Thursday, Sep 24, 2020 - - - -

Seminar in Philosophical Logic
Thursday, Sep 24, 6:30 PM.
(Zoom link upon request RParikh@gc.cuny.edu; will be sent automatically to seminar members)
Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY
Coherent Judgment: Previsions and Forecasts

Abstract. This talk is to continue critical discussion of Persi Diaconis and Brian Skyrms' book chapter, "Judgment," from their Ten Great Ideas about Chance (Princeton University Press, 2018). Specifically, I will cover two variations on coherence advanced by de Finetti to justify his theory of personal probability, each cast in game-theoretic terms — one based on previsions, the other based on forecasting. I will show how his ideas extend both conceptually and mathematically to subsequent developments due to Savage, Anscombe & Aumann, and others. While the talk is to be self-contained, an excellent reference for broader discussion is Peter Fishburn's "Utility and Subjective Probability: Contemporary Theories," International Encyclopedia of the Social & Behavioral Sciences, 2001: 16113-16121.

- - - - Friday, Sep 25, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Sep 25, 11am

The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Ralf Schindler, University of Münster
Martin's Maximum^++ implies the P_max axiom (*)

Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.

Next Week in Logic at CUNY:

- - - - Monday, Sep 28, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, September 29st, 4.15-6.15 (NY time)

For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Daniel Hoek (Virginia Tech)
Title: Coin flips, Spinning Tops and the Continuum Hypothesis

Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).

- - - - Tuesday, Sep 29, 2020 - - - -

- - - - Wednesday, Sep 30, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Sep 30, 2:00pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Leszek Kołodziejczyk University of Warsaw
Ramsey's Theorem over RCA∗0RCA0∗: Part II

Abstract: The usual base theory used in reverse mathematics, RCA0RCA0, is the fragment of second-order arithmetic axiomatized by Δ01Δ10 comprehension and Σ01Σ10 induction. The weaker base theory RCA∗0RCA0∗ is obtained by replacing Σ01Σ10 induction with Δ01Δ10 induction (and adding the well-known axiom expexp in order to ensure totality of the exponential function). In first-order terms, RCA0RCA0 is conservative over IΣ1IΣ1 and RCA∗0RCA0∗ is conservative over BΣ1+expBΣ1+exp.

Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0RCA0∗.

Given standard natural numbers n,k≥2n,k≥2, let RTnkRTkn stand for Ramsey's Theorem for kk-colourings of nn-tuples. We first show that assuming the failure of Σ01Σ10 induction, RTnkRTkn is equivalent to its own relativization to an arbitrary Σ01Σ10-definable cut. Using this, we give a complete axiomatization of the first-order consequences of RCA∗0+RTnkRCA0∗+RTkn for n≥3n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of RT2kRTk2. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of RT22RT22 over the traditional base theory RCA0RCA0.

In the first part of the talk, we concentrated on Ramsey's Theorem for nn-tuples where n≥3n≥3. In this second part, the focus will be on RT22RT22.

The New York City Category Theory Seminar
Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html

Speaker: David Ellerman, University of Ljubljana.
Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.

Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps.
Paper: Available here http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf

- - - - Thursday, Oct 1, 2020 - - - -

- - - - Friday, Oct 2, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 2, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

David Aspero, University of East Anglia

TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

This Week in Logic at CUNY

9/20/2020 21:54:11

This Week in Logic at CUNY:

- - - - Monday, Sep 21, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, September 21st, 4.15-6.15 (NY time)

For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Yale Weiss (CUNY)
Title: Arithmetical Semantics for Non-Classical Logic

Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.

- - - - Tuesday, Sep 22, 2020 - - - -

- - - - Wednesday, Sep 23, 2020 - - - -

- - - - Thursday, Sep 24, 2020 - - - -

Seminar in Philosophical Logic
Thursday, Sep 24, 6:30 PM.
(Zoom link upon request RParikh@gc.cuny.edu; will be sent automatically to seminar members)
Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY
Coherent Judgment: Previsions and Forecasts

Abstract. This talk is to continue critical discussion of Persi Diaconis and Brian Skyrms' book chapter, "Judgment," from their Ten Great Ideas about Chance (Princeton University Press, 2018). Specifically, I will cover two variations on coherence advanced by de Finetti to justify his theory of personal probability, each cast in game-theoretic terms — one based on previsions, the other based on forecasting. I will show how his ideas extend both conceptually and mathematically to subsequent developments due to Savage, Anscombe & Aumann, and others. While the talk is to be self-contained, an excellent reference for broader discussion is Peter Fishburn's "Utility and Subjective Probability: Contemporary Theories," International Encyclopedia of the Social & Behavioral Sciences, 2001: 16113-16121.

- - - - Friday, Sep 25, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Sep 25, 11am

The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Ralf Schindler, University of Münster
Martin's Maximum^++ implies the P_max axiom (*)

Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.

Next Week in Logic at CUNY:

- - - - Monday, Sep 28, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, September 29st, 4.15-6.15 (NY time)

For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Daniel Hoek (Virginia Tech)
Title: Coin flips, Spinning Tops and the Continuum Hypothesis

Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).

- - - - Tuesday, Sep 29, 2020 - - - -

- - - - Wednesday, Sep 30, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Sep 30, 2:00pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Leszek Kołodziejczyk University of Warsaw
Ramsey's Theorem over $R C A * 0$ : Part II

Abstract: The usual base theory used in reverse mathematics, $R C A 0$ , is the fragment of second-order arithmetic axiomatized by $Δ 01$ comprehension and $Σ 01$ induction. The weaker base theory $R C A * 0$ is obtained by replacing $Σ 01$ induction with $Δ 01$ induction (and adding the well-known axiom $exp$ in order to ensure totality of the exponential function). In first-order terms, $R C A 0$ is conservative over $I Σ 1$ and $R C A * 0$ is conservative over $B Σ 1 + exp$ .

Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over $R C A * 0$ .

Given standard natural numbers

n, k \geq 2

, let

R T n k

stand for Ramsey's Theorem for

k

-colourings of

n

-tuples. We first show that assuming the failure of

Σ 01

induction,

R T n k

is equivalent to its own relativization to an arbitrary

Σ 01

-definable cut. Using this, we give a complete axiomatization of the first-order consequences of

R C A * 0 + R T n k

for

n \geq 3

(this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of

R T 2 k

. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of

R T 22

over the traditional base theory

R C A 0

.

In the first part of the talk, we concentrated on Ramsey's Theorem for $n$ -tuples where $n \geq 3$ . In this second part, the focus will be on $R T 22$ .

The New York City Category Theory Seminar
Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html

Speaker: David Ellerman, University of Ljubljana.
Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.

Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps.
Paper: Available here http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf

- - - - Thursday, Oct 1, 2020 - - - -

- - - - Friday, Oct 2, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Oct 2, 3pm

The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

David Aspero, University of East Anglia

TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

9/20/2020 10:49:20

Dear all, Because of the current COVID-19 epidemic related restrictions there will be no seminar next week, Wednesday September 23 (students are now officially not allowed to participate seminars). As for the following weeks, we will see how he situation develops. Best, David

Roman Kossak: Truth, Resplendence, and Directed Graphs with Local Finite Height

Boise Logic and Set Theory Seminar

9/17/2020

[Email the organizer scoskey@boisestate.edu for Zoom meeting number] Speaker: Roman Kossak (CUNY) Title: Truth, Resplendence, and Directed Graphs with Local Finite Height Abstract: Under certain assumptions, a nonstandard model of arithmetic admits an assignment of truth values for all of its sentences, standard and nonstandard. This important result in the model theory of arithmetic was proved in 1981 by Kotlarski, Krajewski and Lachlan, with a proof employing a ``rather exotic proof-theoretic technology." In 2009, Enayat and Viser gave a much more accessible model-theoretic proof. In 2018, Schmerl isolated the graph-theoretic component of the Enayat-Visser proof, by showing that certain infinite graphs have kernels, from which the theorem can be obtained as a straightforward corollary. This story is an excellent example of how mathematics gets simplified. I will explain all basic concepts and I will outline the proof of Shmerl's result. Schmerl's paper is at: arXiv:1807.11832

Tagged: Roman Kossak

Logic Seminar 16 Sept 2020 17:00 hrs at NUS by Ye Jinhe (Notre Dame)

NUS Logic Seminar

9/15/2020 4:23:06

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 16 September 2020, 17:00 hrs Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Speaker: Ye Jinhe Title: The etale open topology URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: For any field K, we introduce natural topologies on K-points of varieties over K, which is defined to be the weakest topology such that etale morphisms are open. This topology turns out to be natural in a lot of settings. For example, when K is algebraically closed, it is easy to see that we have the Zariski topology and it picks up the valuation topology in many Henselian valued fields. Moreover, many topological properties correspond to the algebraic properties of the field. As an application, we will show large stable fields are separably closed, a special case of the stable fields conjecture. This is joint work with Will Johnson, Chieu-Minh Tran and Erik Walsberg.

This Week in Logic at CUNY

9/13/2020 22:31:31

This Week in Logic at CUNY:

- - - - Monday, Sep 14, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, September 14th, 4.15-6.15
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Chris Scambler (NYU)
Title: Cantor’s Theorem, Modalized

Abstract: I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.

- - - - Tuesday, Sep 15, 2020 - - - -

Computational Logic Seminar
Fall 2020, on-line meetings
Please send me a request for a link to this talk - Sergei Artemov (sartemov@gc.cuny.edu)
Time 2:00 - 4:00 PM Tuesday
September 15, 2020
Speaker: Sergei Artemov, Graduate Center, City University of New York
Title: On Constructive Epistemic Logic

Abstract: A joint paper: S.Artemov and T.Protopopescu, Intuitionistic Epistemic Logic, The Review of Symbolic Logic 9(2):266-298, 2016,
opened the door to a new avenue of active research in constructive epistemic logic. We will present the basics and comment on the current state of these studies.

- - - - Wednesday, Sep 16, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Sep 16, 5:00pm

The seminar will take place virtually at 5pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Sam Coskey, Boise State University
Classification of countable models of ZFC

In 2009 Roman Kossak and I showed that the classification of countable models of PA is Borel complete, which means it is as complex as possible. The proof is a straightforward application of Gaifman’s canonical I-models. In 2017 Sam Dworetzky, John Clemens, and I showed that the argument may also be used to show the classification of countable models of ZFC is Borel complete too. In this talk I'll outline the original argument for models of PA, the adaptation for models of ZFC, and briefly consider several subclasses of countable models of ZFC.

The New York City Category Theory Seminar
Date and Time: Wednesday September 16, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html

Speaker: Rick Jardine, University of Western Ontario.

Title: Posets, metric spaces, and topological data analysis.

Abstract: Traditional TDA is the analysis of homotopy invariants of systems of spaces V(X) that arise from finite metric spaces X, via distance measures. These spaces can be expressed in terms of posets, which are barycentric subdivisions of the usual Vietoris-Rips complexes V(X). The proofs of stability theorems in TDA are sharpened considerably by direct use of poset techniques.

Expanding the domain of definition to extended pseudo metric spaces enables the construction of a realization functor on diagrams of spaces, which has a right adjoint Y |--> S(Y), called the singular functor. The realization of the Vietoris-Rips system V(X) for an ep-metric space X is the space itself. The counit of the adjunction defines a map \eta: V(X) --> S(X), which is a sectionwise weak equivalence - the proof uses simplicial approximation techniques.

This is the context for the Healy-McInnes UMAP construction, which will be discussed if time permits. UMAP is non-traditional: clusters for UMAP are defined by paths through sequences of neighbour pairs, which can be a highly efficient process in practice.

- - - - Thursday, Sep 17, 2020 - - - -

Zoom seminar in Philosophical Logic
Contact Rohit Parikh (rparikh@gc.cuny.edu) for zoom link.

Thursday September 17 at 6:30 PM
Larry Moss of Indiana University will speak about Judgment from

the recent book by Diaconis and Skyrms

- - - - Friday, Sep 18, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Sep 18, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Arthur Apter, CUNY
UA and the Number of Normal Measures over ℵω+1ℵω+1
The Ultrapower Axiom UA, introduced by Goldberg and Woodin, is known to have many striking consequences. In particular, Goldberg has shown that assuming UA, the Mitchell ordering of normal measures over a measurable cardinal is linear. I will discuss how this result may be used to construct choiceless models of ZF in which the number of normal measures at successors of singular cardinals can be precisely controlled.

Next Week in Logic at CUNY:

- - - - Monday, Sep 21, 2020 - - - -

- - - - Tuesday, Sep 22, 2020 - - - -

- - - - Wednesday, Sep 23, 2020 - - - -

- - - - Thursday, Sep 24, 2020 - - - -

- - - - Friday, Sep 25, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Sep 25, 11am

The seminar will take place virtually at 11am US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Ralf Schindler, University of Münster
Martin's Maximum^++ implies the P_max axiom (*)

Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

9/13/2020 8:47:47

Dear all, Mirna Džamonja (IHPST CNRS-Université Panthéon-Sorbonne, Paris) will be visiting the Institute of Mathematics CAS during the upcoming week. She will give talks both at the Set Theory and Analysis seminar on Tuesday September 15th at 10 AM and the at the Wednesday seminar. The announcement for the Tuesday seminar is here: https://calendar.math.cas.cz/set-theory-and-analysis-actual The Seminar on Reckoning meets on Wednesday September 16th at 11:00 in the Institute of Mathematics CAS, Zitna 25. !!! In order to be able to comply with the current 2 meters separation rule the seminar changes location next week. We will meet in the blue lecture room on the ground floor of the rear building. !!! Program: Mirna Džamonja -- On wide Aronszajn trees Aronszajn trees are a staple of set theory, but there are applications where the requirement of all levels being countable is of no importance. This is the case in set-theoretic model theory, where trees of height and size ω1 but with no uncountable branches play an important role by being clocks of Ehrenfeucht--Fraïssé games that measure similarity of model of size ℵ1. We call such trees wide Aronszajn. In this context one can also compare trees T and T’ by saying that T weakly embeds into T’ if there is a function f that map T into T’ while preserving the strict order <_T. This order translates into the comparison of winning strategies for the isomorphism player, where any winning strategy for T’ translates into a winning strategy for T’. Hence it is natural to ask if there is a largest such tree, or as we would say, a universal tree for the class of wood Aronszajn trees with weak embeddings. It was known that there is no such a tree under CH, but in 1994 Mekler and Väänanen conjectured that there would be under MA(ω1). In our upcoming JSL paper with Saharon Shelah we prove that this is not the case: under MA(ω1) there is no universal wide Aronszajn tree. The talk will discuss that paper. The paper is available on the arxiv and on line at JSL in the preproof version DOI: 10.1017/jsl.2020.42 Best, David

Wednesday seminar

Prague Set Theory Seminar

9/13/2020 8:47:47

Dear all, Mirna Džamonja (IHPST CNRS-Université Panthéon-Sorbonne, Paris) will be visiting the Institute of Mathematics CAS during the upcoming week. She will give talks both at the Set Theory and Analysis seminar on Tuesday September 15th at 10 AM and the at the Wednesday seminar. The announcement for the Tuesday seminar is here: https://calendar.math.cas.cz/set-theory-and-analysis-actual The Seminar on Reckoning meets on Wednesday September 16th at 11:00 in the Institute of Mathematics CAS, Zitna 25. !!! In order to be able to comply with the current 2 meters separation rule the seminar changes location next week. We will meet in the blue lecture room on the ground floor of the rear building. !!! Program: Mirna Džamonja -- On wide Aronszajn trees Aronszajn trees are a staple of set theory, but there are applications where the requirement of all levels being countable is of no importance. This is the case in set-theoretic model theory, where trees of height and size ω1 but with no uncountable branches play an important role by being clocks of Ehrenfeucht--Fraïssé games that measure similarity of model of size ℵ1. We call such trees wide Aronszajn. In this context one can also compare trees T and T’ by saying that T weakly embeds into T’ if there is a function f that map T into T’ while preserving the strict order <_T. This order translates into the comparison of winning strategies for the isomorphism player, where any winning strategy for T’ translates into a winning strategy for T’. Hence it is natural to ask if there is a largest such tree, or as we would say, a universal tree for the class of wood Aronszajn trees with weak embeddings. It was known that there is no such a tree under CH, but in 1994 Mekler and Väänanen conjectured that there would be under MA(ω1). In our upcoming JSL paper with Saharon Shelah we prove that this is not the case: under MA(ω1) there is no universal wide Aronszajn tree. The talk will discuss that paper. The paper is available on the arxiv and on line at JSL in the preproof version DOI: 10.1017/jsl.2020.42 Best, David

Wednesday seminar

Prague Set Theory Seminar

9/7/2020 4:39:58

Dear all, The seminar meets on Wednesday September 9th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. The program is not yet determined, walk-in speakers are welcome. Otherwise we have the usual backup option of me talking about something.. Best, David

Kyoto University Research Institute for Mathematical Sciences Set Theory Workshop, November 16-20, 2020

Conference

9/7/2020

Kyoto University Research Institute for Mathematical Sciences Set Theory Workshop 2020 Set Theory: Reals and Topology November 16-20, 2020 http://strims2020.sa-suke.com Call for lectures and participation Due to the COVID-19 pandemic, the workshop will take place online. This is the first online version of this workshop. Every year, set theory researchers from Japan and abroad gather at the RIMS (Research Institute for Mathematical Sciences) of Kyoto University and hold an international workshop that brings together both expert and young researchers of set theory. As indicated in the title “Set Theory: Reals and Topology”, the main topic this year is about the developments of set theory and its interaction with combinatorics of the reals and topology. We encourage both young researchers and experts, from Japan and abroad, to contribute with lectures in any topic of Set Theory (not necessarily in the main topic). We expect participation (even without lecture) of many researchers in the area and graduate students. Registration is required for participation (see details on the webpage). Registration deadlines: For contributed lectures: October 1st, 2020. For participation (without lecture): October 15th, 2020. Minicourse Speakers Osvaldo Guzmán (Universidad Nacional Autónoma de México) Ashutosh Kumar (Indian Institute of Technology Kampur) Invited Speakers Martin Goldstern (TU Wien) Ulises Ariet Ramos-García (Universidad Nacional Autónoma de México) Organizer: Diego A. Mejía (Shizuoka University) Scientific Committee: Teruyuki Yorioka (Shizuoka University) Dilip Raghavan (National University of Singapore)

https://us02web.zoom.us/j/89623455996?pwd=b0JsL2JVeVBrV1AzTVJ6dWNYNkx2dz09

Tagged: Osvaldo Guzmán, Ashutosh Kumar, Martin Goldstern, Ulises Ariet Ramos-García, Diego A. Mejía

This Week in Logic at CUNY

9/6/2020 20:28:03

This Week in Logic at CUNY:

- - - - Monday, Sep 7, 2020 - - - -

- - - - Tuesday, Sep 8, 2020 - - - -

************************
Computational Logic Seminar
Fall 2020, on-line meetings
Time 2:00 - 4:00 PM Tuesday, September 8, 2020
Please send a request for a link to this talk (unless you are registered of have already sent me a request for the whole semester): sartemov@gc.cuny.edu
Speaker: Melvin Fitting, Graduate Center, City University of New York
Title: About `Binding Modalities'

Abstract:
In classical logic the addition of quantifiers to propositional logic is essentially unique, with some minor variations of course. In modal logic things are not so monolithic. One can quantify over things or over intensions; domains can be the same from possible world to possible world, or shrink, or grow, or follow no pattern, as one moves from a possible world to an accessible one. In 1963 Kripke showed that shrinking or growing domains related to validity of the Barcan and the converse Barcan formulas, but this was a semantic result. Proof theory is trickier. Nested sequents are well behaved, but axiom systems can be unruly. A direct combination of propositional modal axioms and rules with standard quantificational axioms and rules simply proves the converse Barcan formula. It's not easy to get rid of it. Kripke showed how one could do so, but he needed to use a less common axiomatization of the quantifiers. It works, but one has the impression of having a formal proof system with road blocks placed carefully to prevent proofs from veering into the ditch. Some 40 or more years later, justification logic was created by Artemov, and now there are justification systems that correspond to infinitely many different modal logics. The first justification logic was called LP, for logic of proofs. It is related to propositional S4. LP was extended to a quantified version by Artemov and Yavorskaya, with a possible world semantics supplied by Fitting. Subsequently Artemov and Yavorskaya transferred their ideas, concerning what they called binding modalities, back from quantified LP to quantified S4 itself. In the present work we carry their ideas on further to the basic normal modal logic, K, which is not as well-behaved as S4 on these matters. It turns out that this provides a natural intuition for Kripke's non-standard axiomatization from those many years ago. It also relates quite plausibly to the distinction between de re and de dicto. But now the main work is done through a generalization of the modal operator, instead of through a restriction on allowed quantifier axiomatizations.

- - - - Wednesday, Sep 9, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Sep 9, 3:00pm

The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Saeideh Bahrami, Institute for Research in Fundamental Sciences, Tehran
Fixed Points of Initial Self-Embeddings of Models of Arithmetic
In 1973, Harvey Friedman proved his striking result on initial self-embeddings of countable nonstandard models of set theory and Peano arithmetic. In this talk, I will discuss my joint work with Ali Enayat focused on the fixed point set of initial self-embeddings of countable nonstandard models of arithmetic. Especially, I will survey the proof of some generalizations of well-known results on the fixed point set of automorphisms of countable recursively saturated models of PAPA, to results about the fixed point set of initial self-embeddings of countable nonstandard models of IΣ1IΣ1.

- - - - Thursday, Sep 10, 2020 - - - -

- - - - Friday, Sep 11, 2020 - - - -

Next Week in Logic at CUNY:

- - - - Monday, Sep 14, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, September 14th, 4.15-6.15
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Chris Scambler (NYU)
Title: Cantor’s Theorem, Modalized

Abstract: I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.

- - - - Tuesday, Sep 15, 2020 - - - -

- - - - Wednesday, Sep 16, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Sep 16, 5:00pm

The seminar will take place virtually at 5pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Sam Coskey, Boise State University
TBA

- - - - Thursday, Sep 17, 2020 - - - -

- - - - Friday, Sep 18, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Sep 18, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Arthur Apter, CUNY
UA and the Number of Normal Measures over $ℵ ω + 1$
The Ultrapower Axiom UA, introduced by Goldberg and Woodin, is known to have many striking consequences. In particular, Goldberg has shown that assuming UA, the Mitchell ordering of normal measures over a measurable cardinal is linear. I will discuss how this result may be used to construct choiceless models of ZF in which the number of normal measures at successors of singular cardinals can be precisely controlled.

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Logic Seminar 9 Sept 2020 17:00 hrs at NUS by Ming Xiao

NUS Logic Seminar

8/31/2020 21:45:54

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 9 September 2020, 17:00 hrs Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Speaker: Ming Xiao Title: A Borel Chain Condition of T(X) URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: In 1948, Horn and Tarski conjectured whether the sigma-finite chain condition and sigma-bounded chain condition are equivalent. The first counterexample was given by Thummel in 2012 and then a Borel counterexample was given by Todorvevic in 2014. Both examples belong to a class of poset called "Todorvevic ordering" T(X) over topological spaces X. In this talk, I will illustrate a satisfactory condition for a topological space X making the corresponding poset T(X) fail to have a countable Borel partition witnessing the sigma-finite chain condition, although it may still be witnessed by non-Borel partitions. The content of this talk is going to be the same as the one I gave in a seminar at the Chinese Academy of Sciences last year and is also a part of my Ph.D. dissertation.

This Week in Logic

This Week in Logic at CUNY

8/30/2020 22:30:02

Hi everyone,

Classes started at CUNY last week, and regular mailings of this newsletter will continue through the Fall semester. Please let me know if you have logic-related events at CUNY or elsewhere that you would like to include.

Best regards,

Jonas Reitz

jreitz@nylogic.org

This Week in Logic at CUNY:

- - - - Monday, Aug 31, 2020 - - - -

- - - - Tuesday, Sep 1, 2020 - - - -

- - - - Wednesday, Sep 02, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Sep 2, 3:00pm

The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

September 2
Petr Glivický, Universität Salzburg
The $ω$ -iterated nonstandard extension of $N$ and Ramsey combinatorics

In the theory of nonstandard methods (traditionally known as nonstandard analysis), each mathematical object (a set) $x$ has a uniquely determined so called nonstandard extension $* x$ . In general, $* x ⊋ {* y; y \in x}$ - that is, besides the original 'standard' elements $* y$ for $y \in x$ , the set $* x$ contains some new 'nonstandard' elements.

For instance, some of the nonstandard elements of $* R$ can be interpreted as infinitesimals (there is $ε \in * R$ such that $0 < ε < 1 / n$ for all $n \in N$ ) allowing for nonstandard analysis to be developed in $* R$ , while $* N$ turns out to be an (at least $ℵ 1$ -saturated) nonstandard elementary extension of $N$ (in the language of arithmetic).

While the whole nonstandard real analysis is most naturally developed in $* R$ (with just a few advanced topics where using the second extension $* * R$ is convenient, though far from necessary), recent successful applications of nonstandard methods in combinatorics on $N$ have utilized also higher order extensions $(n) * N = * * * \dots * N$ with the chain $* * * \dots *$ of length $n > 2$ .

In this talk we are going to study the structure of the $ω$ -iterated nonstandard extension $\cdot N = ⋃ n \in ω (n) * N$ of $N$ and show how the obtained results shed new light on the complexities of Ramsey combinatorics on $N$ and allow us to drastically simplify proofs of many advanced Ramsey type theorems such as Hindmann's or Milliken's and Taylor's.

- - - - Thursday, Sep 03, 2020 - - - -

Seminar in philosophical logic

Thursday, Sep 3, 6:30pm

Rohit Parikh, City University of New York

On September 3 I will give a talk in the Zoom seminar in philosophical logic which takes place on Thursdays at 6:30 PM.

I will speak about the Sorites paradox and vagueness, relying on previous work by Michael Dummett, Kit Fine, Lotfi Zadeh and myself. I hope you will find it enjoyable.

Join Zoom Meeting

Meeting ID: 896 2345 5996

Passcode: 143539

- Rohit Parikh

- - - - Friday, Sep 04, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Sep 4, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Mirna Džamonja, IHPST, CNRS-Université Panthéon-Sorbonne Paris, France
On logics that make a bridge from the Discrete to the Continuous
We study logics which model the passage between an infinite sequence of finite models to an uncountable limiting object, such as is the case in the context of graphons. Of particular interest is the connection between the countable and the uncountable object that one obtains as the union versus the combinatorial limit of the same sequence.

Next Week in Logic at CUNY:

- - - - Monday, Sep 7, 2020 - - - -

- - - - Tuesday, Sep 8, 2020 - - - -

- - - - Wednesday, Sep 9, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, Sep 9, 3:00pm

The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Saeideh Bahrami, Institute for Research in Fundamental Sciences, Tehran
Fixed Points of Initial Self-Embeddings of Models of Arithmetic
In 1973, Harvey Friedman proved his striking result on initial self-embeddings of countable nonstandard models of set theory and Peano arithmetic. In this talk, I will discuss my joint work with Ali Enayat focused on the fixed point set of initial self-embeddings of countable nonstandard models of arithmetic. Especially, I will survey the proof of some generalizations of well-known results on the fixed point set of automorphisms of countable recursively saturated models of

P A

, to results about the fixed point set of initial self-embeddings of countable nonstandard models of

I Σ 1

.

7/26/2020 22:59:40

This Week in Logic at CUNY:

- - - - Monday, Jul 27, 2020 - - - -

- - - - Tuesday, Jul 28, 2020 - - - -

- - - - Wednesday, Jul 29, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, July 29, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Kameryn Williams, University of Hawai‘i at Mānoa
End-extensions of models of set theory and the Σ1Σ1 universal finite sequence

Recall that if M⊆NM⊆N are models of set theory then NN end-extends MM if NN does not have new elements for sets in MM. In this talk I will discuss a Σ1Σ1-definable finite sequence which is universal for end extensions in the following sense. Consider a computably axiomatizable extension ¯¯¯¯¯¯¯ZFZF¯ of ZFZF. There is a Σ1Σ1-definable finite sequencea0,a1,…,ana0,a1,…,anwith the following properties.

* ZFZF proves that the sequence is finite.
* In any transitive model of ¯¯¯¯¯¯¯ZFZF¯ the sequence is empty.
* If MM is a countable model of ¯¯¯¯¯¯¯ZFZF¯ in which the sequence is ss and t∈Mt∈M is a finite sequence extending ss then there is an end-extension N⊨¯¯¯¯¯¯¯ZFN⊨ZF¯ of MM in which the sequence is exactly tt.
* Indeed, for the previous statements it suffices that M⊨ZFM⊨ZF and end-extends a submodel W⊨¯¯¯¯¯¯¯ZFW⊨ZF¯ of height at least (ωL1)M(ω1L)M.

This universal finite sequence can be used to determine the modal validities of end-extensional set-theoretic potentialism, namely to be exactly the modal theory S4S4. The sequence can also be used to show that every countable model of set theory extends to a model satisfying the end-extensional maximality principle, asserting that any possibly necessary sentence is already true.

This talk is about joint work with Joel David Hamkins. The Σ1Σ1 universal finite sequence is a sister to the Σ2Σ2 universal finite sequence for rank-extensions of Hamkins and Woodin, and both are cousins of Woodin's universal algorithm for arithmetic.

- - - - Thursday, Jul 30, 2020 - - - -

- - - - Friday, Jul 31, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, July 31, 12pm

The seminar will take place virtually at 12pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.

Corey Switzer, CUNY
Dissertation defense: Alternative Cichoń diagrams and forcing axioms compatible with CH
This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from ωωωω to ωωωω. I prove that these cardinals can be organized into two diagrams analogous to the standard Cichoń diagram show several independence results and investigate their relation to cardinal invariants on omega. In the second half of the thesis I look at forcing axioms compatible with CH. First I consider Jensen's subcomplete and subproper forcing. I generalize these notions to larger classes which are (apparently) much more nicely behaved structurally. I prove iteration and preservation theorems for both classes and use these to produce many new models of the subcomplete forcing axiom. Finally I deal with dee-complete forcing and its associated axiom DCFA. Extending a well-known result of Shelah, I show that if a tree of height ω1ω1 with no branch can be embedded into an ω1ω1 tree, possibly with uncountable branches, then it can be specialized without adding reals. As a consequence I show that DCFA implies there are no Kurepa trees, even if CH fails.

Next Week in Logic at CUNY:

- - - - Monday, Aug 3, 2020 - - - -

- - - - Tuesday, Aug 4, 2020 - - - -

- - - - Wednesday, Aug 5, 2020 - - - -

- - - - Thursday, Aug 6, 2020 - - - -

- - - - Friday, Aug 7, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, Aug 7, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.

Brent Cody, Virginia Commonwealth University

TBA

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

7/22/2020 10:21:05

Dear all, The seminar meets on Wednesday July 29th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Egbert Thümmel -- There are no tall analytic Ramsey ideals An ideal I on omega is said to be Ramsey if the partition relation I^+ -> (I^+)_2^2 does hold. Answering a question of Hrušák and Thümmel, we show that there are no tall analytic Ramsey ideals. We also show that every analytic ideal is either included in an F_sigma ideal, or it has a restriction which is Katětov-above the ideal generated by convergent sequences of rationals. Best, David

Logic summer school at Fudan University, August 10-21, 2020

Conference

7/21/2020

We are organising a logic summer school at Fudan University from Aug 10 - Aug 21. It will be delivered via Zoom meeting. In the first week, Prof. Renling Jin will talk about nonstandard analysis (please note that this part will be in Chinese). In the second week, Prof. Ralf Schindler will introduce the proof of Woodin's (∗) axiom from Martin's Maximum++. Participants are encouraged to fill a registration form, and we will send the Zoom meeting ID accordingly. For more information, we have a webpage for the summer school: http://logic.fudan.edu.cn/event2020/summer.

Tagged: Renling Jin, Ralf Schindler

This Week in Logic at CUNY

7/19/2020 22:25:59

This Week in Logic at CUNY:

- - - - Monday, Jul 20, 2020 - - - -

- - - - Tuesday, Jul 21, 2020 - - - -

- - - - Wednesday, Jul 22, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, July 22, 8:00pm

The seminar will take place virtually at 8pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Tin Lok Wong, National University of Singapore
Properties preserved in cofinal extensions
Cofinal extensions generally preserve many more properties of a model of arithmetic than their sisters, end extensions. Exactly how much must or can they preserve? The answer is intimately related to how much arithmetic the model can do. I will survey what is known and what is not known about this question, and report on some recent work on this line.

Video

- - - - Thursday, Jul 23, 2020 - - - -

- - - - Friday, Jul 24, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, July 24, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.

Andrew Brooke-Taylor, University of Leeds
Measurable cardinals and limits in the category of sets
An old result of Isbell characterises measurable cardinals in terms of certain canonical limits in the category of sets. After introducing this characterisation, I will talk about recent work with Adamek, Campion, Positselski and Rosicky teasing out the importance of the canonicity for this and related results. The language will be category-theoretic but the proofs will be quite hands-on combinatorial constructions with sets.

Next Week in Logic at CUNY:

- - - - Monday, Jul 27, 2020 - - - -

- - - - Tuesday, Jul 28, 2020 - - - -

- - - - Wednesday, Jul 29, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, July 29, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Kameryn Williams, University of Hawai‘i at Mānoa
End-extensions of models of set theory and the $Σ 1$ universal finite sequence

Recall that if $M \subseteq N$ are models of set theory then $N$ end-extends $M$ if $N$ does not have new elements for sets in $M$ . In this talk I will discuss a $Σ 1$ -definable finite sequence which is universal for end extensions in the following sense. Consider a computably axiomatizable extension $¯ ¯¯¯¯¯ ¯ Z F$ of $Z F$ . There is a $Σ 1$ -definable finite sequence $a 0, a 1, \dots, a n$ with the following properties.

* $Z F$ proves that the sequence is finite.
* In any transitive model of $¯ ¯¯¯¯¯ ¯ Z F$ the sequence is empty.
* If $M$ is a countable model of $¯ ¯¯¯¯¯ ¯ Z F$ in which the sequence is $s$ and $t \in M$ is a finite sequence extending $s$ then there is an end-extension $N ⊨ ¯ ¯¯¯¯¯ ¯ Z F$ of $M$ in which the sequence is exactly $t$ .
* Indeed, for the previous statements it suffices that $M ⊨ Z F$ and end-extends a submodel $W ⊨ ¯ ¯¯¯¯¯ ¯ Z F$ of height at least $(ω L 1) M$ .

This universal finite sequence can be used to determine the modal validities of end-extensional set-theoretic potentialism, namely to be exactly the modal theory $S 4$ . The sequence can also be used to show that every countable model of set theory extends to a model satisfying the end-extensional maximality principle, asserting that any possibly necessary sentence is already true.

This talk is about joint work with Joel David Hamkins. The $Σ 1$ universal finite sequence is a sister to the $Σ 2$ universal finite sequence for rank-extensions of Hamkins and Woodin, and both are cousins of Woodin's universal algorithm for arithmetic.

- - - - Thursday, Jul 30, 2020 - - - -

- - - - Friday, Jul 31, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, July 31, 12pm

The seminar will take place virtually at 12pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.

Corey Switzer, CUNY
Dissertation defense: Alternative Cichoń diagrams and forcing axioms compatible with CH
This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from

ω ω

to

ω ω

. I prove that these cardinals can be organized into two diagrams analogous to the standard Cichoń diagram show several independence results and investigate their relation to cardinal invariants on omega. In the second half of the thesis I look at forcing axioms compatible with CH. First I consider Jensen's subcomplete and subproper forcing. I generalize these notions to larger classes which are (apparently) much more nicely behaved structurally. I prove iteration and preservation theorems for both classes and use these to produce many new models of the subcomplete forcing axiom. Finally I deal with dee-complete forcing and its associated axiom DCFA. Extending a well-known result of Shelah, I show that if a tree of height

ω 1

with no branch can be embedded into an

ω 1

tree, possibly with uncountable branches, then it can be specialized without adding reals. As a consequence I show that DCFA implies there are no Kurepa trees, even if CH fails.

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

7/17/2020 5:41:13

Dear all, The seminar meets on Wednesday July 22nd at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: David Chodounsky -- Big Ramsey degrees of hypergraphs I will talk about recent developments concerning Big Ramsey degrees of universal homogeneous hypergraphs. In particular, we may go through a proof that these are finite in the 3-uniform case. Best, David

Wednesday seminar

Prague Set Theory Seminar

7/10/2020 10:08:15

Dear all, The seminar meets on Wednesday July 15th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: David Uhrik will talk about the paper of Stevo Todorcevic: Erdős–Kakutani phenomena for paths (attached). Best, David

This Week in Logic at CUNY

7/6/2020 11:13:37

This Week in Logic at CUNY:

- - - - Monday, Jul 6, 2020 - - - -

- - - - Tuesday, Jul 7, 2020 - - - -

- - - - Wednesday, Jul 8, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, July 8, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Corey Switzer, CUNY
Axiomatizing Kaufmann models in strong logics
A Kaufmann model is an ω1ω1-like, recursively saturated, rather classless model of PA. Such models were constructed by Kaufmann under the ♢♢ assumption and then shown to exist in ZFC by Shelah using an absoluteness argument involving the logic Lω1,ω(Q)Lω1,ω(Q) where QQ is the quantifier 'there exists uncountably many…'. It remains an intriguing, if vague, open problem whether one can construct a Kaufmann model in ZFC 'by hand' i.e. without appealing to some form of absoluteness or other very non-constructive methods. In this talk I consider the related problem of axiomatizing Kaufmann models in Lω1,ω(Q)Lω1,ω(Q) and show that this is independent of ZFC. Along the way we'll see that it is also independent of ZFC whether there is an ω1ω1-preserving forcing notion adding a truth predicate to a Kaufmann model.

- - - - Thursday, Jul 9, 2020 - - - -

- - - - Friday, Jul 10, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, July 10, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.

Peter Holy, University of Udine
Uniform large cardinal characterizations and ideals up to measurability

Many prominent large cardinal notions up to measurability can be characterized by the existence of certain ultrafilters for small models of set theory. Most prominently, this includes weakly compact, ineffable, Ramsey and completely ineffable cardinals, but there are many more, and our characterization schemes also give rise to many new natural large cardinal concepts. Moreover, these characterizations allow for the uniform definition of ideals associated to these large cardinals, which agree with the ideals from the set-theoretic literature (for example, the weakly compact, the ineffable, the Ramsey or the completely ineffable ideal) whenever such had been previously established. For many large cardinal notions, we can show that their ordering with respect to direct implication, but also with respect to consistency strength corresponds in a very canonical way to certain relations between their corresponding large cardinal ideals. This is all material from a fairly extensive joint paper with Philipp Luecke, and I will try to provide an overview as well as present some particular results from this paper.

Next Week in Logic at CUNY:

- - - - Monday, Jul 13, 2020 - - - -

- - - - Tuesday, Jul 14, 2020 - - - -

- - - - Wednesday, Jul 15, 2020 - - - -

- - - - Thursday, Jul 16, 2020 - - - -

- - - - Friday, Jul 17, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, July 17, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.

TBA
Kaethe Minden Bard College at Simon's Rock

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

7/6/2020 4:37:07

Dear all, The seminar meets on Wednesday July 8th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Jan Grebik -- Approximate measurable colorings We prove that there is an approximate version of Konig's line coloring theorem and show how to use it to deduce the result of Toth https://arxiv.org/abs/1906.03137 about Schreier decorations. Best, David

Tagged: Jan Grebik

No seminar this week

Toronto Set Theory Seminar

7/2/2020 17:22:00

Hi everyone,

There won't be a seminar this week.

The regular seminar has concluded for this year and will pick up again in the fall. However, if someone would like to speak soon, let me know and I would be happy to organize something.

Have a good summer,

Bill

Wednesday seminar

Prague Set Theory Seminar

6/29/2020 4:40:27

Dear all, There is no seminar this Wednesday due to vacations, next week it is most likely going to be the same story (unless announced otherwise). Working mathematicians can instead join e.g. the online seminars in Jerusalem and Gainesville. HUJI seminar Wednesday July 1, 10:00 CEST In the next few weeks Tzoor Plotinikov will present Neeman construction of a model in which Aleph_{omega+1} has the tree property. Zoom link: https://huji.zoom.us/j/243676331?pwd=dU02bUVaNC9jRCtvc2lKbVJJZ2lFdz09 Meeting ID: 243 676 331 Password: 058372 University of Florida Logic Seminar Tuesday June 30, 22:05 CEST Jordi Lopez-Abad: The Banakh-Sack rank of a weakly compact set abstract attached Zoom link: https://ufl.zoom.us/s/7401025557 Best, David

This Week in Logic at CUNY

6/28/2020 19:36:06

This Week in Logic at CUNY:

- - - - Monday, Jun 29, 2020 - - - -

- - - - Tuesday, Jun 30, 2020 - - - -

- - - - Wednesday, Jul 1, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, July 1, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part II

In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:

1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.

Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.

- - - - Thursday, Jul 2, 2020 - - - -

- - - - Friday, Jul 3, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, July 3, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.

Vera Fischer, University of Vienna
More ZFC inequalities between cardinal invariants

We will discuss some recent ZFC results concerning the generalized Baire spaces, and more specifically the generalized bounding number, relatives of the generalized almost disjointness number, as well as generalized reaping and domination.

Next Week in Logic at CUNY:

- - - - Monday, Jul 6, 2020 - - - -

- - - - Tuesday, Jul 7, 2020 - - - -

- - - - Wednesday, Jul 8, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, July 8, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Corey Switzer, CUNY
Axiomatizing Kaufmann models in strong logics
A Kaufmann model is an $ω 1$ -like, recursively saturated, rather classless model of PA. Such models were constructed by Kaufmann under the $♢$ assumption and then shown to exist in ZFC by Shelah using an absoluteness argument involving the logic $L ω 1, ω (Q)$ where $Q$ is the quantifier 'there exists uncountably many…'. It remains an intriguing, if vague, open problem whether one can construct a Kaufmann model in ZFC 'by hand' i.e. without appealing to some form of absoluteness or other very non-constructive methods. In this talk I consider the related problem of axiomatizing Kaufmann models in $L ω 1, ω (Q)$ and show that this is independent of ZFC. Along the way we'll see that it is also independent of ZFC whether there is an $ω 1$ -preserving forcing notion adding a truth predicate to a Kaufmann model.

- - - - Thursday, Jul 9, 2020 - - - -

- - - - Friday, Jul 10, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, July 10, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.

Peter Holy, University of Udine
TBA

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

This Week in Logic at CUNY

6/21/2020 22:54:01

This Week in Logic at CUNY:

- - - - Monday, Jun 22, 2020 - - - -

- - - - Tuesday, Jun 23, 2020 - - - -

- - - - Wednesday, Jun 24, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, June 24, 2:00pm NOTE: 2:00pm START TIME

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Bartosz Wcisło, Polish Academy of Sciences
Tarski boundary III

Truth theories investigate the notion of truth using axiomatic methods. To a fixed base theory (typically Peano Arithmetic $P A$ ) we add a unary predicate $T (x)$ with the intended interpretation ' $x$ is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.

One of the aspects which we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this demarcating line between conservative and non-conservative truth theories 'the Tarski boundary.'

Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over $P A$ or exactly equivalent to the principle of global reflection over $A$ . It says that sentences provable in $P A$ are true in the sense of the predicate $T$ . This in turn is equivalent to $Δ 0$ induction for the compositional truth predicate which turns out to be a surprisingly robust theory.

The equivalences between nonconservative truth theories are typically proved by relatively direct ad hoc arguments. However, certain patterns seem common to these proofs. The first one is construction of various arithmetical partial truth predicates which provably in a given theory have better properties than the original truth predicate. The second one is deriving induction for these truth predicates from internal induction, a principle which says that for any arithmetical formula, the set of those elements for which that formula is satisfied under the truth predicate satisfies the usual induction axioms.

As an example of this phenomenon, we will present two proofs. First, we will show that global reflection principle is equivalent to local induction. Global reflection expresses that any sentence provable in $P A$ is true. Local induction says that any predicate obtained by restricting truth predicate to sentences of a fixed syntactic complexity $c$ satisfies full induction. This is an observation due to Mateusz Łełyk and the author of this presentation.

The second example is a result by Ali Enayat who showed that $C T 0$ , a theory compositional truth with $Δ 0$ induction, is arithmetically equivalent to the theory of compositional truth together with internal induction and disjunctive correctness.

This talk is intended as a continuation of 'Tarski boundary II' presentation at the same seminar. However, we will try to avoid excessive assumptions on familiarity with the previous part.

- - - - Thursday, Jun 25, 2020 - - - -

- - - - Friday, Jun 26, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, June 26, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Joel David Hamkins, Oxford University
Categorical cardinals
Zermelo famously characterized the models of second-order Zermelo-Fraenkel set theory

ZFC 2

in his 1930 quasi-categoricity result asserting that the models of

ZFC 2

are precisely those isomorphic to a rank-initial segment

V κ

of the cumulative set-theoretic universe

V

cut off at an inaccessible cardinal

κ .

I shall discuss the extent to which Zermelo's quasi-categoricity analysis can rise fully to the level of categoricity, in light of the observation that many of the

V κ

universes are categorically characterized by their sentences or theories. For example, if

κ

is the smallest inaccessible cardinal, then up to isomorphism

V κ

is the unique model of

ZFC 2

plus the sentence 'there are no inaccessible cardinals.' This cardinal

κ

is therefore an instance of what we call a first-order sententially categorical cardinal. Similarly, many of the other inaccessible universes satisfy categorical extensions of

ZFC 2

by a sentence or theory, either in first or second order. I shall thus introduce and investigate the categorical cardinals, a new kind of large cardinal. This is joint work with Robin Solberg (Oxford).

Next Week in Logic at CUNY:

- - - - Monday, Jun 29, 2020 - - - -

- - - - Tuesday, Jun 30, 2020 - - - -

- - - - Wednesday, Jul 1, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, July 1, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part II

In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:

1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.

Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.

- - - - Thursday, Jul 2, 2020 - - - -

- - - - Friday, Jul 3, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, July 3, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.

Vera Fischer, University of Vienna
TBA

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Set theory seminar this week: Will Brian

Toronto Set Theory Seminar

6/21/2020 11:28:00

Hi everyone,

This week, Will Brian (UNC Charlotte) will speak in the seminar. His title and abstract can be found below.

Title: Limited-information strategies in Banach-Mazur games.

Abstract: The Banach-Mazur game is an infinite-length game played on a topological space X, in which two players take turns choosing members of an infinite decreasing sequence of open sets, the first player trying to ensure that the intersection of this sequence is empty, and the second that it is not. A limited-information strategy for one of the players is a game plan that, on any given move, depends on only a small part of the game's history. In this talk we will discuss Telgársky's conjecture, which asserts roughly that there must be topological spaces where winning strategies for the Banach-Mazur game cannot be too limited, but must rely on large parts of the game's history in a significant way. Recently, it was shown that this conjecture fails in models of set theory satisfying GCH + $\Box$ . In such models it is always possible for one player to code all information concerning a game's history into a small piece of it. We will discuss these so-called coding strategies, why assuming GCH + $\Box$ makes them work so well, and what can go wrong in other models of set theory.

The talk will take place on Friday, June 26 from 1:30-3:00 pm EDT on Zoom, follow the link below:

See you there,

Bill

Wednesday seminar

Prague Set Theory Seminar

6/19/2020 8:37:06

Dear all, The seminar meets on Wednesday June 24th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Again, the program is not fixed yet, the backup is either me or Egbert talking about some set theory. (Last time we were looking at the triangle free Henson graph and some new proofs of Ramsey-like properties.) Best, David

Set theory seminar this week: David Schrittesser

Toronto Set Theory Seminar

6/15/2020 13:45:22

Hi everyone,

This week, David Schrittesser (KGRC, University of Vienna) will speak in the seminar.

Title: Higher degrees of madness

Abstract: The notion of mad family can be generalized by replacing the finite ideal by an iterated Fubini product of the finite ideal. While these ideals are more complicated both combinatorially and in terms of Borel complexity, it turns out that the same assumptions of Ramsey theoretic regularity can rule out their existence. We sketch a proof of this and some related results. This talk is a sequel to my last talk at the Fields Institute Seminar.

The talk will take place on Friday, June 19 from 1:30-3:00 pm EDT on Zoom, follow the link below:

See you there,

Bill

This Week in Logic at CUNY

6/14/2020 20:10:03

This Week in Logic at CUNY:

- - - - Monday, Jun 15, 2020 - - - -

- - - - Tuesday, Jun 16, 2020 - - - -

- - - - Wednesday, Jun 17, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, June 17, 2:00pm NOTE: 2:00pm START TIME

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Mateusz Łełyk, University of Warsaw
Partial Reflection over Uniform Disquotational Truth

In the context of arithmetic, a reflection principle for a theory Th is a formal way of expressing that all theorems of Th are true. In the presence of a truth predicate for the language of Th this principle can be expressed as a single sentence (called the Global Reflection principle over Th) but most often is met in the form of a scheme consisting of all sentences of the form

∀x(ProvTh(ϕ(˙x))→ϕ(x)).∀x(ProvTh(ϕ(x˙))→ϕ(x)).Obviously such a scheme is not provable in a consistent theory Th. Nevertheless, such soundness assertions are said to provide a natural and justified way of extending ones initial theory.

This perspective is nowadays very fruitfully exploited in the context of formal theories of truth. One of the most basic observations is that strong axioms for the notions of truth follow from formally weak types of axiomatizations modulo reflection principles. In such a way compositional axioms are consequences of the uniform disquotational scheme for for the truth predicate, which is

∀xT(ϕ(˙x))≡ϕ(x).∀xT(ϕ(x˙))≡ϕ(x).

The above observation is also used in the recent approach to ordinal analysis of theories of predicative strength by Lev Beklemishev and Fedor Pakhomov. The assignment of ordinal notations to theories proceeds via partial reflection principles (for formulae of a fixed ΣnΣn complexity) over (iterated) disquotational scheme. It becomes important to relate theories of this form to fragments of standard theories of truth, in particular the ones based on induction for restricted classes of formulae such as CT0CT0 (the theory of compositional truth with Δ0Δ0-induction for the extended language. The theory was discussed at length in Bartek Wcisło's talk). Beklemishev and Pakhomov leave the following open question:

Is Σ1Σ1-reflection principle over the uniform disquotational scheme provable in CT0CT0?

The main goal of our talk is to present the proof of the affirmative answer to this question. The result significantly improves the known fact on the provability of Global Reflection over PA in CT0CT0. During the talk, we explain the theoretical context described above including the information on how the result fits into Beklemishev-Pakhomov project. In the meantime we give a different proof of their characterisation of Δ0Δ0-reflection over the disquotational scheme.

Despite the proof-theoretical flavour of these results, our proofs rests on essentially model-theoretical techniques. The important ingredient is the Arithmetized Completeness Theorem.

- - - - Thursday, Jun 18, 2020 - - - -

- - - - Friday, Jun 19, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, June 19, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Boban Velickovic, University of Paris 7

Strong guessing models

The notion of a guessing model introduced by Viale and Weiss. The principle $G M (ω 2, ω 1)$ asserts that there are stationary many guessing models of size $ℵ 1$ in $H θ$ , for all large enough regular $θ$ . It follows from $P F A$ and implies many of its structural consequences, however it does not settle the value of the continuum. In search of higher of forcing axioms it is therefore natural to look for extensions and higher versions of this principle. We formulate and prove the consistency of one such statement that we call $S G M + (ω 3, ω 1)$ .
It has a number of important structural consequences:

- the tree property at $ℵ 2$ and $ℵ 3$
- the failure of various weak square principles
- the Singular Cardinal Hypothesis
- Mitchell’s Principle: the approachability ideal agrees with the non stationary ideal on the set of $cof (ω 1)$ ordinals in $ω 2$
- Souslin’s Hypothesis
- The negation of the weak Kurepa Hypothesis
- Abraham’s Principles: every forcing which adds a subset of $ω 2$ either adds a real or collapses some cardinals, etc.

The results are joint with my PhD students Rahman Mohammadpour.

Next Week in Logic at CUNY:

- - - - Monday, Jun 22, 2020 - - - -

- - - - Tuesday, Jun 23, 2020 - - - -

- - - - Wednesday, Jun 24, 2020 - - - -

- - - - Thursday, Jun 25, 2020 - - - -

- - - - Friday, Jun 26, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, June 26, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman for meeting id.
Joel David Hamkins, Oxford University
TBA

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

6/12/2020 7:56:09

Dear all, The seminar will meet again next week, on Wednesday June 17th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. The program is not yet fixed, the default backup is either me or Egbert Thuemmel talking about definable ideals on omega. Best, David

Set theory seminar this week: Jamal Kawach

Toronto Set Theory Seminar

6/8/2020 12:33:06

Hi everyone,

This week, Jamal Kawach (U of T) will speak in the seminar.

Title: Dual Ramsey theory for countable ordinals

Abstract: Using techniques from the theory of topological Ramsey spaces, we prove a dual Ramsey theorem for countable ordinals. Specifically, for each countable ordinal $\alpha$ we define a topological Ramsey space of equivalence relations on $\omega$ which code equivalence relations on $\alpha$ , up to a necessary restriction on the set of minimal representatives of the equivalence classes. This extends the classical dual Ramsey theorem of Carlson and Simpson. This is joint work with Stevo Todorcevic.

The talk will take place on June 12 from 1:30-3:00 pm EDT on Zoom, follow the link below:

See you there,

Bill

This Week in Logic at CUNY

6/7/2020 22:13:02

This Week in Logic at CUNY:

- - - - Monday, Jun 8, 2020 - - - -

- - - - Tuesday, Jun 9, 2020 - - - -

- - - - Wednesday, Jun 10, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, June 10, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:

1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.

Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.

- - - - Thursday, Jun 11, 2020 - - - -

- - - - Friday, Jun 12, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, June 12, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Michał Godziszewski, Munich Center for Mathematical Philosophy
Michał Godziszewski, Munich Center for Mathematical Philosophy
The Multiverse, Recursive Saturation and Well-Foundedness Mirage: Part II
Recursive saturation, introduced by J. Barwise and J. Schlipf is a robust notion which has proved to be important for the study of nonstandard models (in particular, it is ubiquitous in the model theory of axiomatic theories of truth, e.g. in the topic of satisfaction classes, where one can show that if

M ⊨ Z F C

is a countable

ω

-nonstandard model, then

M

admits a satisfaction class iff

M

is recursively saturated). V. Gitman and J. Hamkins showed in A Natural Model of the Multiverse Axioms that the collection of countable, recursively saturated models of set theory satisfy the so-called Hamkins's Multiverse Axioms. The property that forces all the models in the Multiverse to be recursively saturated is the so-called Well-Foundedness Mirage axiom which asserts that every universe is

ω

-nonstandard from the perspective of some larger universe, or to be more precise, that: if a model

M

is in the multiverse then there is a model

N

in the multiverse such that

M

is a set in

N

and

N ⊨' M is ω - nonstandard.'

. Inspection of the proof led to a question if the recursive saturation could be avoided in the Multiverse by weakening the Well-Foundedness Mirage axiom. Our main results answer this in the positive. We give two different versions of the Well-Foundedness Mirage axiom - what we call Weak Well-Foundedness Mirage (saying that if

M

is a model in the Multiverse then there is a model

N

in the Multiverse such that

M \in N

and

N ⊨' M is nonstandard.'

.) and Covering Well-Foundedness Mirage (saying that if

M

is a model in the Multiverse then there is a model

N

in the Multiverse with

K \in N

such that

K

is an end-extension of

M

and

N ⊨' K is ω - nonstandard.'

). I will present constructions of two different Multiverses satisfying these two weakened axioms. This is joint work with V. Gitman. T. Meadows and K. Williams.

Next Week in Logic at CUNY:

- - - - Monday, Jun 15, 2020 - - - -

- - - - Tuesday, Jun 16, 2020 - - - -

- - - - Wednesday, Jun 17, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, June 17, 2:00pm NOTE: 2:00pm START TIME

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Mateusz Łełyk, University of Warsaw
Partial Reflection over Uniform Disquotational Truth

In the context of arithmetic, a reflection principle for a theory Th is a formal way of expressing that all theorems of Th are true. In the presence of a truth predicate for the language of Th this principle can be expressed as a single sentence (called the Global Reflection principle over Th) but most often is met in the form of a scheme consisting of all sentences of the form

\forall x (Prov Th (ϕ (˙ x)) \to ϕ (x)) .

Obviously such a scheme is not provable in a consistent theory Th. Nevertheless, such soundness assertions are said to provide a natural and justified way of extending ones initial theory.

This perspective is nowadays very fruitfully exploited in the context of formal theories of truth. One of the most basic observations is that strong axioms for the notions of truth follow from formally weak types of axiomatizations modulo reflection principles. In such a way compositional axioms are consequences of the uniform disquotational scheme for for the truth predicate, which is

\forall x T (ϕ (˙ x)) \equiv ϕ (x) .

The above observation is also used in the recent approach to ordinal analysis of theories of predicative strength by Lev Beklemishev and Fedor Pakhomov. The assignment of ordinal notations to theories proceeds via partial reflection principles (for formulae of a fixed $Σ n$ complexity) over (iterated) disquotational scheme. It becomes important to relate theories of this form to fragments of standard theories of truth, in particular the ones based on induction for restricted classes of formulae such as $CT 0$ (the theory of compositional truth with $Δ 0$ -induction for the extended language. The theory was discussed at length in Bartek Wcisło's talk). Beklemishev and Pakhomov leave the following open question:

Is

Σ 1

-reflection principle over the uniform disquotational scheme provable in

CT 0

?

The main goal of our talk is to present the proof of the affirmative answer to this question. The result significantly improves the known fact on the provability of Global Reflection over PA in $CT 0$ . During the talk, we explain the theoretical context described above including the information on how the result fits into Beklemishev-Pakhomov project. In the meantime we give a different proof of their characterisation of $Δ 0$ -reflection over the disquotational scheme.

Despite the proof-theoretical flavour of these results, our proofs rests on essentially model-theoretical techniques. The important ingredient is the Arithmetized Completeness Theorem.

- - - - Thursday, Jun 18, 2020 - - - -

- - - - Friday, Jun 19, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, June 19, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Boban Velickovic University of Paris 7

TBA

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

This Week in Logic at CUNY

6/1/2020 20:41:19

This Week in Logic at CUNY:

- - - - Monday, Jun 1, 2020 - - - -

- - - - Tuesday, Jun 2, 2020 - - - -

- - - - Wednesday, Jun 3, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, June 3, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part I

In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:

1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.

Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.

- - - - Thursday, Jun 4, 2020 - - - -

- - - - Friday, Jun 5, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, June 5, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Michał Godziszewski, Munich Center for Mathematical Philosophy
TBA

Next Week in Logic at CUNY:

- - - - Monday, Jun 8, 2020 - - - -

- - - - Tuesday, Jun 9, 2020 - - - -

- - - - Wednesday, Jun 10, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, June 10, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:

1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.

Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.

- - - - Thursday, Jun 11, 2020 - - - -

- - - - Friday, Jun 12, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, June 12, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Michał Godziszewski, Munich Center for Mathematical Philosophy
TBA

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

UPDATE - This Week in Logic at CUNY

This Week in Logic at CUNY

5/25/2020 23:23:22

A correction - this Wednesday's talk in the MOPA seminar will take place at 2pm, rather than the usual 7pm.

Best,

Jonas

This Week in Logic at CUNY:

- - - - Monday, May 25, 2020 - - - -

- - - - Tuesday, May 26, 2020 - - - -

- - - - Wednesday, May 27, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, May 27, 2:00pm

NOTE: New time this week only
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Bartosz Wcisło, University of Warsaw
Tarski boundary II

Truth theories investigate the notion of truth with axiomatic methods. To a fixed base theory (typically Peano Arithmetic PAPA) we add a unary predicate T(x)T(x) with the intended interpretation 'xx is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.

One of the aspects we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this 'demarcating line' between conservative and non-conservative truth theories 'the Tarski boundary.'

Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PAPA or exactly equivalent to the principle of global reflection over PAPA. It says that sentences provable in PAPA are true in the sense of the predicate TT. This in turn is equivalent to Δ0Δ0 induction for the compositional truth predicate which turns out to be a surprisingly robust theory.

In our talk, we will try to sketch proofs representative of research on Tarski boundary. We will present the proof by Enayat and Visser showing that the compositional truth predicate is conservative over PAPA. We will also try to discuss how this proof forms a robust basis for further conservativeness results.

On the non-conservative side of Tarski boundary, the picture seems less organised, since more arguments are based on ad hoc constructions. However, we will try to show some themes which occur rather repeatedly in these proofs: iterated truth predicates and the interplay between properties of good truth-theoretic behaviour and induction. To this end, we will present the argument that disjunctive correctness together with the internal induction principle for a compositional truth predicate yields the same consequences as Δ0Δ0-induction for the compositional truth predicate (as proved by Ali Enayat) and that it shares arithmetical consequences with global reflection. The presented results are currently known to be suboptimal.

This talk is intended as a continuation of 'Tarski boundary' presentation. However, we will try to avoid excessive assumptions on familiarity with the previous part.

- - - - Thursday, May 28, 2020 - - - -

- - - - Friday, May 29, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 29, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Kameryn Williams, University of Hawai‘i at Mānoa
The geology of inner mantles

An inner model is a ground if V is a set forcing extension of it. The intersection of the grounds is the mantle, an inner model of ZFC which enjoys many nice properties. Fuchs, Hamkins, and Reitz showed that the mantle is highly malleable. Namely, they showed that every model of set theory is the mantle of a bigger, better universe of sets. This then raises the possibility of iterating the definition of the mantle—the mantle, the mantle of the mantle, and so on, taking intersections at limit stages—to obtain even deeper inner models. Let's call the inner models in this sequence the inner mantles.

In this talk I will present some results about the sequence of inner mantles, answering some questions of Fuchs, Hamkins, and Reitz. Specifically, I will present the following results, analogues of classic results about the sequence of iterated HODs.

1. (Joint with Reitz) Consider a model of set theory and consider an ordinal eta in that model. Then this model has a class forcing extension whose eta-th inner mantle is the model we started out with, where the sequence of inner mantles does not stabilize before eta.

2. It is consistent that the omega-th inner mantle is an inner model of ZF + ¬AC.

3. It is consistent that the omega-th inner mantle is not a definable class, and indeed fails to satisfy Collection.

Next Week in Logic at CUNY:

- - - - Monday, Jun 1, 2020 - - - -

- - - - Tuesday, Jun 2, 2020 - - - -

- - - - Wednesday, Jun 3, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, June 3, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part I

In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:

1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.

Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.

- - - - Thursday, Jun 4, 2020 - - - -

- - - - Friday, Jun 5, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, June 5, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Michał Godziszewski, Munich Center for Mathematical Philosophy
TBA

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

This Week in Logic at CUNY

5/25/2020 21:55:51

Hi everyone,

The CUNY semester is coming to an end. However, a number of seminars have plans to continue into the summer months. Regular weekly mailings of "This Week in Logic at CUNY" will continue as long as we have events to report!

Best regards,

Jonas

This Week in Logic at CUNY:

- - - - Monday, May 25, 2020 - - - -

- - - - Tuesday, May 26, 2020 - - - -

- - - - Wednesday, May 27, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, May 27, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Bartosz Wcisło, University of Warsaw
Tarski boundary II

Truth theories investigate the notion of truth with axiomatic methods. To a fixed base theory (typically Peano Arithmetic $P A$ ) we add a unary predicate $T (x)$ with the intended interpretation ' $x$ is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.

One of the aspects we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this 'demarcating line' between conservative and non-conservative truth theories 'the Tarski boundary.'

Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over $P A$ or exactly equivalent to the principle of global reflection over $P A$ . It says that sentences provable in $P A$ are true in the sense of the predicate $T$ . This in turn is equivalent to $Δ 0$ induction for the compositional truth predicate which turns out to be a surprisingly robust theory.

In our talk, we will try to sketch proofs representative of research on Tarski boundary. We will present the proof by Enayat and Visser showing that the compositional truth predicate is conservative over $P A$ . We will also try to discuss how this proof forms a robust basis for further conservativeness results.

On the non-conservative side of Tarski boundary, the picture seems less organised, since more arguments are based on ad hoc constructions. However, we will try to show some themes which occur rather repeatedly in these proofs: iterated truth predicates and the interplay between properties of good truth-theoretic behaviour and induction. To this end, we will present the argument that disjunctive correctness together with the internal induction principle for a compositional truth predicate yields the same consequences as $Δ 0$ -induction for the compositional truth predicate (as proved by Ali Enayat) and that it shares arithmetical consequences with global reflection. The presented results are currently known to be suboptimal.

This talk is intended as a continuation of 'Tarski boundary' presentation. However, we will try to avoid excessive assumptions on familiarity with the previous part.

- - - - Thursday, May 28, 2020 - - - -

- - - - Friday, May 29, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 29, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Kameryn Williams, University of Hawai‘i at Mānoa
The geology of inner mantles

An inner model is a ground if V is a set forcing extension of it. The intersection of the grounds is the mantle, an inner model of ZFC which enjoys many nice properties. Fuchs, Hamkins, and Reitz showed that the mantle is highly malleable. Namely, they showed that every model of set theory is the mantle of a bigger, better universe of sets. This then raises the possibility of iterating the definition of the mantle—the mantle, the mantle of the mantle, and so on, taking intersections at limit stages—to obtain even deeper inner models. Let's call the inner models in this sequence the inner mantles.

In this talk I will present some results about the sequence of inner mantles, answering some questions of Fuchs, Hamkins, and Reitz. Specifically, I will present the following results, analogues of classic results about the sequence of iterated HODs.

1. (Joint with Reitz) Consider a model of set theory and consider an ordinal eta in that model. Then this model has a class forcing extension whose eta-th inner mantle is the model we started out with, where the sequence of inner mantles does not stabilize before eta.

2. It is consistent that the omega-th inner mantle is an inner model of ZF + ¬AC.

3. It is consistent that the omega-th inner mantle is not a definable class, and indeed fails to satisfy Collection.

Next Week in Logic at CUNY:

- - - - Monday, Jun 1, 2020 - - - -

- - - - Tuesday, Jun 2, 2020 - - - -

- - - - Wednesday, Jun 3, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, June 3, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part I

In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:

1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.

Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.

- - - - Thursday, Jun 4, 2020 - - - -

- - - - Friday, Jun 5, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, June 5, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Michał Godziszewski, Munich Center for Mathematical Philosophy
TBA

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Set theory seminar this week: Michael Hrusak

Toronto Set Theory Seminar

5/25/2020 10:59:31

Hi everyone,

This Friday, Michael Hrusak (UNAM) will speak in our seminar on the Invariant Ideal Axiom.

Abstract: We introduce the Invariant Ideal Axiom and discuss its impact on the structure of countable topological groups. (joint work with Alexander Shibakov)

The talk will take place on May 29 from 1:30-3:00 pm EDT on Zoom, follow the link below:

Bill Chen

Set theory seminar this week: Vinicius de Oliveira Rodrigues

Toronto Set Theory Seminar

5/18/2020 9:32:37

Hi everyone,

This week, the seminar will host Vinicius de Oliveira Rodrigues (University of São Paulo) who will speak about "Pseudocompact hyperspaces of Isbell-Mrówka spaces." The talk will feature some new results obtained after his talk from November.

Abstract: J. Ginsburg has asked what is the relation between the pseudocompactness of the $\omega$ -th power of a topological space $X$ and the pseudocompactness of its Vietoris Hyperspace, $\exp(X)$ . M. Hrusak, I. Martínez-Ruiz and F. Hernandez-Hernandez studied this question restricted to Isbell-Mrówka spaces, that is, spaces of the form $\Psi(A)$ where A is an almost disjoint family. Regarding these spaces, if $\exp(X)$ is pseudocompact, then $X^\omega$ is also pseudocompact, and $X^\omega$ is pseudocompact iff $A$ is a MAD family. They showed that if the cardinal characteristic $\mathfrak{p}$ is $\mathfrak{c}$ , then for every MAD family $A$ , $\exp(\Psi(A))$ is pseudocompact, and if the cardinal characteristic $\mathfrak{h}$ is less than $\mathfrak{c}$ , there exists a MAD family $A$ such that $\exp(\Psi(A))$ is not pseudocompact. They asked if there exists a MAD family $A$ (in ZFC) such that $\exp(\Psi(A))$ is pseudocompact.

In this talk, we present some new results on the (consistent) existence of MAD families whose hyperspaces of their Isbell-Mrówka spaces are (or are not) pseudocompact by constructing new examples. Moreover, we give some combinatorial equivalences for every Isbell-Mrówka space from a MAD family having pseudocompact hyperspace. This is a joint work with, O. Guzman, M. Hrusak, S. Todorcevic and A. Tomita.

The talk will take place this Friday, May 22, from 1:30-3:00 pm EDT on Zoom, follow the link below:

Bill Chen

This Week in Logic at CUNY

5/17/2020 23:27:42

This Week in Logic at CUNY:

- - - - Monday, May 18, 2020 - - - -

- - - - Tuesday, May 19, 2020 - - - -

- - - - Wednesday, May 20, 2020 - - - -

- - - - Thursday, May 21, 2020 - - - -

- - - - Friday, May 22, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 15, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part II

A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.

In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.

Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).

Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality:
(a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M.
Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.

Next Week in Logic at CUNY:

- - - - Monday, May 25, 2020 - - - -

- - - - Tuesday, May 26, 2020 - - - -

- - - - Wednesday, May 27, 2020 - - - -

- - - - Thursday, May 28, 2020 - - - -

- - - - Friday, May 29, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 22, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Kameryn Williams, University of Hawai‘i at Mānoa
TBA

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

This Week in Logic at CUNY

5/10/2020 21:15:38

This Week in Logic at CUNY:

- - - - Monday, May 11, 2020 - - - -

- - - - Tuesday, May 12, 2020 - - - -

- - - - Wednesday, May 13, 2020 - - - -

MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 13

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Laurence Kirby, CUNY

Bounded finite set theory

There is a well-known close logical connection between PA and finite set theory. Is there a set theory that corresponds in an analogous way to bounded arithmetic $I Δ 0$ ? I propose a candidate for such a theory, called $I Δ 0 S$ , and consider the questions: what set-theoretic axioms can it prove? And given a model M of $I Δ 0$ is there a model of $I Δ 0 S$ whose ordinals are isomorphic to M? The answer is yes if M is a model of Exp; to obtain the answer we use a new way of coding sets by numbers.

- - - - Thursday, May 14, 2020 - - - -

- - - - Friday, May 15, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 15, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part I

A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.

In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.

Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).

Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality:
(a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M.
Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.

Next Week in Logic at CUNY:

- - - - Monday, May 18, 2020 - - - -

- - - - Tuesday, May 19, 2020 - - - -

- - - - Wednesday, May 20, 2020 - - - -

- - - - Thursday, May 21, 2020 - - - -

- - - - Friday, May 22, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 15, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part II

A model MM of set theory is said to be 'condensable' if there is an 'ordinal' αα of MM such that the rank initial segment of MM determined by αα is both isomorphic to MM, and an elementary submodel of MM for infinitary formulae appearing in the well-founded part of MM. Clearly if MM is condensable, then MM is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.

In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.

Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model MM of ZFC which has the property that every definable element of MM is in the well-founded part of MM (in particular, MM is ωω-standard, and therefore not recursively saturated).

Theorem 2. The following are equivalent for an ill-founded model MM of ZF of any cardinality:
(a) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' αα of MM such that the rank initial segment of MM determined by αα is an elementary submodel of MM for infinitary formulae appearing in the well-founded part of M.M.
Moreover, if MM is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) MM is expandable to Gödel-Bernays class theory plus Δ11Δ11-Comprehension + Σ12Σ21-Choice.

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Online seminars and talks in Logic

A list of existing seminar series with talks available online, and links to recorded talks:

http://lagrange.math.siu.edu/calvert/OnlineLogicSeminar.html

Online Logic Seminar at SIU

Computability Theory and Applications

Oxford Set Theory Seminar

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Set theory seminar this Friday: Dima Sinapova

Toronto Set Theory Seminar

5/5/2020 8:00:00

Hi everyone,

This week, we will have Dima Sinapova speaking in the seminar. Her talk is entitled "Iteration, reflection, and Prikry forcing."

Abstract: There is an inherent tension between stationary reflection and the failure of SCH. The former is a compactness type principle that follows from large cardinals. The latter is an instance of incompactness, and usually obtained using Prikry forcing. We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we discuss the situation at smaller cardinals. This is joint work with Alejandro Poveda and Assaf Rinot.

The talk will take place this Friday, May 8, from 1:30-3:00 pm EDT on Zoom, follow the link below:

IMPORTANT NOTE: Due to an upgrade in Zoom security features, we have a new Zoom link and Meeting ID. Please change your bookmarks accordingly.

See you there,

Bill Chen

This Week in Logic at CUNY

5/4/2020 0:29:42

Hi everyone,

I'm pleased to pass along the following announcement from Joel David Hamkins:

Oxford Set Theory Seminar
I am starting the Oxford Set Theory Seminar, to be held online via Zoom for the foreseeable future. All set theorists are welcome to participate. You can find a schedule of this term's talks at http://jdh.hamkins.org/oxford-set-theory-seminar/ .

-Joel

Best,
Jonas

This Week in Logic at CUNY:

- - - - Monday, May 4, 2020 - - - -

- - - - Tuesday, May 5, 2020 - - - -

- - - - Wednesday, May 6, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, May 6, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

May 6
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA: Part II

The subject of this two-part talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem $Δ 11 - C A 0$ of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.

As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.

In part I, after going over some history, and preliminaries, I will discuss (1) the gap in the Barwise-Schlipf paper, and (2) the aforementioned Feferman-Stavi proof. In part II, I will focus on how the gap can be circumvented with a proof strategy very different from that Barwise and Schlipf.

- - - - Thursday, May 7, 2020 - - - -

- - - - Friday, May 8, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 8, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Sandra Müller, University of Vienna
TBA

Next Week in Logic at CUNY:

- - - - Monday, May 11, 2020 - - - -

- - - - Tuesday, May 12, 2020 - - - -

- - - - Wednesday, May 13, 2020 - - - -

- - - - Thursday, May 14, 2020 - - - -

- - - - Friday, May 15, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 15, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part I

A model $M$ of set theory is said to be 'condensable' if there is an 'ordinal' $α$ of $M$ such that the rank initial segment of $M$ determined by $α$ is both isomorphic to $M$ , and an elementary submodel of $M$ for infinitary formulae appearing in the well-founded part of $M$ . Clearly if $M$ is condensable, then $M$ is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.

In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.

Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model $M$ of ZFC which has the property that every definable element of $M$ is in the well-founded part of $M$ (in particular, $M$ is $ω$ -standard, and therefore not recursively saturated).

Theorem 2. The following are equivalent for an ill-founded model $M$ of ZF of any cardinality:
(a) $M$ is expandable to Gödel-Bernays class theory plus $Δ 11$ -Comprehension.
(b) There is a cofinal subset of 'ordinals' $α$ of $M$ such that the rank initial segment of $M$ determined by $α$ is an elementary submodel of $M$ for infinitary formulae appearing in the well-founded part of $M .$
Moreover, if $M$ is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) $M$ is expandable to Gödel-Bernays class theory plus $Δ 11$ -Comprehension + $Σ 12$ -Choice.

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

Oxford Set Theory Seminar
See schedule at:

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

https://yorku.zoom.us/j/925557716

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

5/3/2020 14:58:37

Dear all, There are still no seminar in Prague next week. However, the PhD defence of Jan Grebik will take place on Tuesday, May 5th at 10:00 via Zoom, https://cesnet.zoom.us/j/98441831119 The defence is public, guests are welcome and expected. More info here: https://is.cuni.cz/studium/szz_st/index.php?do=detail_kom&kom=28035&term=587734 Let me also add info on the zoom seminars in Jerusalem and Wroclaw next week, these may be relevant for our usual audience. Ziemowit Kostana -- Cohen-like poset for adding Fraisse limits Tuesday May 5, 17:00 CEST https://us02web.zoom.us/j/85273088816?pwd=RnRJcXc1YnpWL3R2Y1JRWkVGRUJxUT09 Meeting ID: 852 7308 8816 Password: 978458 There exist a natural forcing notion which turns given countable set into a Fraisse limit of a given Fraisse class. This long-known phenomenon provided a rough intuition that Fraisse limits, as "generic structures", have some connections with forcing. The goal of the talk is to look at some particular instances and possible applications of this idea. Tsoor Plotnikov -- Proper forcings and side conditions forcings (continued) Monday May 4, 10:00am CEST Meeting ID: 995 0029 0990 Password: 789132 Here are links to the files containing the write up of the two previous talks: https://drive.google.com/file/d/1GkkMmUA8usD-vVw0ybX1M5_eTZhgURcu/view?usp=sharing https://drive.google.com/file/d/1izDqHGMFcGiQw75TvtyD4jzvi7YS-8EW/view?usp=sharing Alejandro Poveda -- Sigma-Prikry forcings and their iterations Wednesday May 6, at 10:00 CEST Meeting ID: 243 676 331 (no password) In a joint project with A. Rinot and D. Sinapova we introduce a class of notions of forcing which we call $\Sigma$-Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality are $\Sigma$-Prikry. Among these examples one may find Prikry forcing and its supercompact version, Gitik-Sharon forcing or the Extender Based Prikry forcing due to Gitik and Magidor. Our first result shows that there is a functor $\mathbb{A}(\cdot,\cdot)$ which, given a $\Sigma$-Prikry poset $\mathbb P$ and a name for a non-reflecting stationary set $\dot{T}$, yields a $\Sigma$-Prikry poset $\mathbb{A}(\mathbb{P},\dot{T})$ that projects onto $\mathbb P$ and kills the stationarity of $T$. Afterwards, we develop a viable iteration scheme for $\Sigma$-Prikry posets. In this talk I pretend to give an overview of this theory and, if time permits, present the very first application of the method: namely, the consistency of a failure of the SCH_\kappa with $Refl(<\omega,\kappa^+)$, where $\kappa$ is a strong limit singular cardinal of countable cofinality. Best, David

Set theory seminar this week: Paul Szeptycki

Toronto Set Theory Seminar

4/29/2020 19:34:05

Hi everyone,

This Friday, Paul Szeptycki will speak in the seminar. His talk is entitled "Strong convergence properties and an example from a $\Box$ sequence."

Abstract: We present an example of a space constructed from $\Box(\kappa)$ answering some questions of Arhangel'skii. Coauthors Bill Chen and Cesar Corral-Rojas.

The talk will take place this Friday, May 1, from 1:30-3:00 pm EDT on Zoom, follow the link below:

See you there,

Bill Chen

This Week in Logic at CUNY

4/26/2020 22:44:39

This Week in Logic at CUNY:

- - - - Monday, Apr 27, 2020 - - - -

- - - - Tuesday, Apr 28, 2020 - - - -

- - - - Wednesday, Apr 29, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, April 29, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

April 29
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA

The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.

As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.

- - - - Thursday, Apr 30, 2020 - - - -

- - - - Friday, May 1, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 1, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Joan Bagaria Universitat de Barcelona
TBA

Next Week in Logic at CUNY:

- - - - Monday, May 4, 2020 - - - -

- - - - Tuesday, May 5, 2020 - - - -

- - - - Wednesday, May 6, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, May 6, 7:00pm

The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

May 6
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA, part 2

The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.

As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.

- - - - Thursday, May 7, 2020 - - - -

- - - - Friday, May 8, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 8, 2pm

The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Sandra Müller, University of Vienna
TBA

- - - - Other Logic News - - - -

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

4/26/2020 7:35:09

Dear all, Still no seminars in Prague next week, I am forwarding info about relevant online seminars and about the PhD thesis defense of Jan Grebik. The Jerusalem basic concepts seminar will continue on Monday April 27th at 11 AM Israel time (= 10 AM CEST). Tsoor Plotnikov will continue the series of talks on Proper forcings and side conditions. The Zoom link for the seminar is Meeting Link: https://huji.zoom.us/j/99500290990?pwd=K0RYOTVHdlUzd2JURys0RVI3Znd0UT09 Meeting ID: 995 0029 0990 Password: 789132 On Tuesday April 28th at 17:00 Aleksandra Kwiatkowska will give a talk on "Simplicity of the automorphism groups of homogeneous structures" at the Wroclaw seminar. If you are interested, ask Piotr Borodulin-Nadzieja or me for the Zoom link. The PhD defense of Jan Grebik will take place next Tuesday, May 5th at 10:00 via Zoom, https://cesnet.zoom.us/j/98441831119 The defense is public, guests are welcome and expected. More info here: https://is.cuni.cz/studium/szz_st/index.php?do=detail_kom&kom=28035&term=587734 Best, David On 16/04/2020 12:40, David Chodounsky wrote: > Dear all, > > Still no seminars seminars in Prague in the foreseeable future. > However, there are interesting set theory online seminar in Jerusalem > next week, see the forwarded email (note that the times refers to the > Israel time zone). > > Best, > David > > > > > -------- Forwarded Message -------- > Subject: Set Theory seminars next week > Date: Wed, 15 Apr 2020 20:38:09 +0000 > From: Menachem Magidor > > > The schedule for the set theory seminars (of course via ZOOM) for next > week is as follows > > 1. *The basic learning seminar > *The seminar will be held on Monday April 20th at 11 am. > Tsur Plotnikov will start a series of talk about side conditions > forcing of two types and PFA. > As introduction the talks will include some basic facts about > proper forcings. > > The Zoom meeting ID for this seminar will be 995 0029 0990 and the > password is 789132 > > > 2. The regular Wednesday seminar will be held on Wednesday April 22nd > at 11 am. > Jing Zhang will speak about > Title: Transformations of the transfinite plane > Abstract: We discuss the existence of certain transformation functions > turning pairs of ordinals into triples (or pairs) of ordinals, that > allows reductions of complicated Ramsey theoretic problems into simpler > ones. We will focus on the existence of various kinds of strong > colorings. The basic technique is Todorcevic's walks on ordinals. Joint > work with Assaf Rinot. > > The Zoom meeting ID is 243-676-331 > and no password. > > Best > Menachem Magidor

Wednesday seminar

Prague Set Theory Seminar

4/26/2020 7:35:09

Dear all, Still no seminars in Prague next week, I am forwarding info about relevant online seminars and about the PhD thesis defense of Jan Grebik. The Jerusalem basic concepts seminar will continue on Monday April 27th at 11 AM Israel time (= 10 AM CEST). Tsoor Plotnikov will continue the series of talks on Proper forcings and side conditions. The Zoom link for the seminar is Meeting Link: https://huji.zoom.us/j/99500290990?pwd=K0RYOTVHdlUzd2JURys0RVI3Znd0UT09 Meeting ID: 995 0029 0990 Password: 789132 On Tuesday April 28th at 17:00 Aleksandra Kwiatkowska will give a talk on "Simplicity of the automorphism groups of homogeneous structures" at the Wroclaw seminar. If you are interested, ask Piotr Borodulin-Nadzieja or me for the Zoom link. The PhD defense of Jan Grebik will take place next Tuesday, May 5th at 10:00 via Zoom, https://cesnet.zoom.us/j/98441831119 The defense is public, guests are welcome and expected. More info here: https://is.cuni.cz/studium/szz_st/index.php?do=detail_kom&kom=28035&term=587734 Best, David On 16/04/2020 12:40, David Chodounsky wrote: > Dear all, > > Still no seminars seminars in Prague in the foreseeable future. > However, there are interesting set theory online seminar in Jerusalem > next week, see the forwarded email (note that the times refers to the > Israel time zone). > > Best, > David > > > > > -------- Forwarded Message -------- > Subject: Set Theory seminars next week > Date: Wed, 15 Apr 2020 20:38:09 +0000 > From: Menachem Magidor > > > The schedule for the set theory seminars (of course via ZOOM) for next > week is as follows > > 1. *The basic learning seminar > *The seminar will be held on Monday April 20th at 11 am. > Tsur Plotnikov will start a series of talk about side conditions > forcing of two types and PFA. > As introduction the talks will include some basic facts about > proper forcings. > > The Zoom meeting ID for this seminar will be 995 0029 0990 and the > password is 789132 > > > 2. The regular Wednesday seminar will be held on Wednesday April 22nd > at 11 am. > Jing Zhang will speak about > Title: Transformations of the transfinite plane > Abstract: We discuss the existence of certain transformation functions > turning pairs of ordinals into triples (or pairs) of ordinals, that > allows reductions of complicated Ramsey theoretic problems into simpler > ones. We will focus on the existence of various kinds of strong > colorings. The basic technique is Todorcevic's walks on ordinals. Joint > work with Assaf Rinot. > > The Zoom meeting ID is 243-676-331 > and no password. > > Best > Menachem Magidor

Set theory seminar this week: Todd Eisworth

Toronto Set Theory Seminar

4/21/2020 13:36:18

Hi everyone,

This Friday, Todd Eisworth (Ohio University) will speak in the seminar on "Representability and pseudopowers."

Abstract: We will prove some basic facts about Shelah’s pseudopower function, and derive some new (?) ZFC results in cardinal arithmetic using basic topological ideas. This talk is designed to be an introduction to this part of pcf theory.

The talk will take place this Friday, April 24, from 1:30-3:00 pm EDT on Zoom, (https://yorku.zoom.us/j/925557716).

See you there,

Bill Chen

This Week in Logic at CUNY

4/19/2020 23:21:46

Hi everyone,

A number of logic seminars worldwide have moved online, which provides an unprecedented opportunity for wide participation. In addition to this newsletter and our own website, nylogic.github.io, take a look at the following for more seminar listings:

European Set Theory Society

List of upcoming online talks in set theory around the world:

Logic Supergroup (UCONN)

An alliance of logicians in quarantine, comprised of logic groups across the world, hosting virtual talks:

http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Best regards,

Jonas

This Week in Logic at CUNY:

- - - - Monday, Apr 20, 2020 - - - -

- - - - Tuesday, Apr 21, 2020 - - - -

- - - - Wednesday, Apr 22, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, April 22, 7:00pm

The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Corey Switzer, CUNY
Hanf Numbers of Arithmetics

Recall that given a complete theory

T

and a type

p (x)

the Hanf number for

p (x)

is the least cardinal

κ

so that any model of

T

of size

κ

realizes

p (x)

(if such a

κ

exists and

\infty

otherwise). The Hanf number for

T

, denoted

H (T)

, is the supremum of the successors of the Hanf numbers for all possible types

p (x)

whose Hanf numbers are

< \infty

. We have seen so far in the seminar that for any complete, consistent

T

in a countable language

H (T) \leq ℶ ω 1

(a result due to Morley). In this talk I will present the following theorems: (1) The Hanf number for true arithmetic is

ℶ ω

(Abrahamson-Harrington-Knight) but (2) the Hanf number for False Arithmetic is

ℶ ω 1

(Abrahamson-Harrington)

- - - - Thursday, Apr 23, 2020 - - - -

- - - - Friday, Apr 24, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, April 24, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Arthur Apter, CUNY

Indestructibility and the First Two Strongly Compact Cardinals

Starting from a model of ZFC with two supercompact cardinals, I will discuss how to force and construct a model in which the first two strongly compact cardinals

κ 1

and

κ 2

are also the first two measurable cardinals. In this model,

κ 1

's strong compactness is indestructible under arbitrary

κ 1

-directed closed forcing, and

κ 2

's strong compactness is indestructible under

A d d (κ 2, λ)

for any ordinal

λ

. This answers a generalized version of a question of Sargsyan.

Next Week in Logic at CUNY:

- - - - Monday, Apr 27, 2020 - - - -

- - - - Tuesday, Apr 28, 2020 - - - -

- - - - Wednesday, Apr 29, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, April 29, 7:00pm

The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

April 29
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA

The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem $Δ 11 - C A 0$ of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.

As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.

- - - - Thursday, Apr 30, 2020 - - - -

- - - - Friday, May 1, 2020 - - - -

Set Theory Seminar

CUNY Graduate Center

Friday, May 1, 2pm

The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Joan Bagaria Universitat de Barcelona
TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

4/16/2020 6:40:24

Dear all, Still no seminars seminars in Prague in the foreseeable future. However, there are interesting set theory online seminar in Jerusalem next week, see the forwarded email (note that the times refers to the Israel time zone). Best, David -------- Forwarded Message -------- Subject: Set Theory seminars next week Date: Wed, 15 Apr 2020 20:38:09 +0000 From: Menachem Magidor The schedule for the set theory seminars (of course via ZOOM) for next week is as follows 1. *The basic learning seminar *The seminar will be held on Monday April 20th at 11 am. Tsur Plotnikov will start a series of talk about side conditions forcing of two types and PFA. As introduction the talks will include some basic facts about proper forcings. The Zoom meeting ID for this seminar will be 995 0029 0990 and the password is 789132 2. The regular Wednesday seminar will be held on Wednesday April 22nd at 11 am. Jing Zhang will speak about Title: Transformations of the transfinite plane Abstract: We discuss the existence of certain transformation functions turning pairs of ordinals into triples (or pairs) of ordinals, that allows reductions of complicated Ramsey theoretic problems into simpler ones. We will focus on the existence of various kinds of strong colorings. The basic technique is Todorcevic's walks on ordinals. Joint work with Assaf Rinot. The Zoom meeting ID is 243-676-331 and no password. Best Menachem Magidor

Wednesday seminar

Prague Set Theory Seminar

4/16/2020 6:40:24

Dear all, Still no seminars seminars in Prague in the foreseeable future. However, there are interesting set theory online seminar in Jerusalem next week, see the forwarded email (note that the times refers to the Israel time zone). Best, David -------- Forwarded Message -------- Subject: Set Theory seminars next week Date: Wed, 15 Apr 2020 20:38:09 +0000 From: Menachem Magidor The schedule for the set theory seminars (of course via ZOOM) for next week is as follows 1. *The basic learning seminar *The seminar will be held on Monday April 20th at 11 am. Tsur Plotnikov will start a series of talk about side conditions forcing of two types and PFA. As introduction the talks will include some basic facts about proper forcings. The Zoom meeting ID for this seminar will be 995 0029 0990 and the password is 789132 2. The regular Wednesday seminar will be held on Wednesday April 22nd at 11 am. Jing Zhang will speak about Title: Transformations of the transfinite plane Abstract: We discuss the existence of certain transformation functions turning pairs of ordinals into triples (or pairs) of ordinals, that allows reductions of complicated Ramsey theoretic problems into simpler ones. We will focus on the existence of various kinds of strong colorings. The basic technique is Todorcevic's walks on ordinals. Joint work with Assaf Rinot. The Zoom meeting ID is 243-676-331 and no password. Best Menachem Magidor

Set theory seminar this week: Matteo Viale

Toronto Set Theory Seminar

4/14/2020 8:00:00

Hi everyone,

This Friday, Matteo Viale (University of Torino) will speak in the seminar. His talk is entitled "Tameness for set theory."

Abstract: We show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic definable concepts of second and third order arithmetic, and appealing to the model-theoretic notions of model completeness and model companionship.

Specifically we develop a general framework linking generic absoluteness results to model companionship and show that (with the required care in details) a $\Pi_2$ -property formalized in an appropriate language for second or third order number theory is forcible from some T extending ZFC + large cardinals if and only if it is consistent with the universal fragment of T if and only if it is realized in the model companion of T.

Part (but not all) of our results are conditional to the proof of Schindler and Asperò that Woodin’s axiom (*) can be forced by a stationary set preserving forcing.

The talk will take place this Friday, April 17, from 1:30-3:00 pm EDT on Zoom, (https://yorku.zoom.us/j/925557716).

There have been efforts to aggregate different logic seminars taking place online by Anton Bernshteyn http://math.cmu.edu/~abernsht/logic_talks_online/ and Miguel Moreno http://miguelmath.com/webminars.html. You might find these resources to be useful.

Have a good week,

Bill Chen

This Week in Logic at CUNY

4/12/2020 21:58:13

Hi everyone,

I'm very pleased to announce that some seminars are continuing virtually during this turbulent time. Regular weekly mailings of "This Week in Logic" will resume until further notice!

Best regards,

Jonas

This Week in Logic at CUNY:

- - - - Monday, Apr 13, 2020 - - - -

- - - - Tuesday, Apr 14, 2020 - - - -

- - - - Wednesday, Apr 15, 2020 - - - -

MOPA (Models of Peano Arithmetic)

CUNY Graduate Center

Wednesday, April 15, 7:00pm

The seminar will take place virtually at 7pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.

Wei Wang, Institute of Logic and Cognition, Sun Yat-sen University
Non-standard models of arithmetic and their standard systems

PA is the first order fragment of Peano's axiomatization of the natural numbers. The natural numbers, N, is called the standard model of PA. But by compactness theorem in first order logic, there are also models of PA different from N, which are called non-standard models of arithmetic. Like in N, every element of a non-standard model M has a binary expansion, which can be regarded as the characteristic function of a subset of N. The standard system of M is the collection of all such subsets of N. It is known that standard systems of non-standard models are always Scott sets and every Scott set of cardinality less than or equal to the first uncountable cardinal is the standard system of some non-standard model. However, the general Scott set problem, whether every Scott set is the standard system of some non-standard model, remains one of the major open problems in the model theory of arithmetic. This talk will present some history of Scott set problem, as well as two constructions of non-standard models with uncountable standard systems.

- - - - Thursday, Apr 16, 2020 - - - -

- - - - Friday, Apr 17, 2020 - - - -

Set Theory Seminar
CUNY Graduate Center
Friday, April 17, 2pm
The seminar will take place virtually at 2pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Corey Switzer, CUNY
Specializing Wide Trees Without Adding Reals

An important advancement in iterated forcing was Jensen’s proof that CH does not imply

♢

by iteratively specializing Aronszajn trees with countable levels without adding reals thus producing a model of CH plus 'all Aronszajn trees are special'. This proof was improved by Shelah who developed a general method around the notion of dee-complete forcing. This class (under certain circumstances) can be iterated with countable support and does not add reals. However, neither Jensen's nor Shelah's posets will specialize trees of uncountable width and it remains unclear when one can iteratively specialize wider trees. Indeed a very intriguing example, due to Todorčević, shows that there is always a wide Aronszajn tree which cannot be specialized without adding reals. By contrast the ccc forcing for specializing Aronszajn trees makes no distinction between trees of different widths (but may add many reals). In this talk we will provide a general criteria a wide trees Aronszajn tree can have that implies the existence of a dee-complete poset specializing it. Time permitting we will discuss applications of this forcing to forcing axioms compatible with CH and some open questions related to set theory of the reals.

Next Week in Logic at CUNY:

- - - - Monday, Apr 20, 2020 - - - -

- - - - Tuesday, Apr 21, 2020 - - - -

- - - - Wednesday, Apr 22, 2020 - - - -

- - - - Thursday, Apr 23, 2020 - - - -

- - - - Friday, Apr 24, 2020 - - - -

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Set theory seminar this week: Keegan Dasilva Barbosa

Toronto Set Theory Seminar

4/7/2020 8:00:00

Hi everyone,

This Friday, Keegan Dasilva Barbosa will speak on A Decomposition Theorem for Aronszajn Lines.

Abstract: We will prove that under the proper forcing axiom, the class of all Aronszajn lines behave like $\sigma$ -scattered orders under the embeddability relation. In particular, we show that the class of better quasi order labeled fragmented Aronszajn lines is itself a better quasi order. Moreover, we show that every better quasi order labeled Aronszajn line can be expressed as a finite sum of labeled types which are algebraically indecomposable. By encoding lines with finite labeled trees, we are also able to deduce a decomposition result, that for every Aronszajn line $L$ , there is an $n\in \omega$ such that for any finite colouring of $L$ , there is a subset $L'$ of $L$ isomorphic to $L$ which uses no more than $n$ colours.

The talk will take place this Friday, April 10, from 1:30-3:00 pm EDT on Zoom, details below:

Join Zoom Meeting
https://yorku.zoom.us/j/925557716

Topic: Set Theory Seminar
Time: Apr 10, 2020 01:30 PM Eastern Time (US and Canada)

19:30 CEST (Central Europe)

01:30 AM SST (Singapore)

Bill Chen

Logic Seminar Wed 8 April 2020 17:00 hrs at NUS via Zoom

NUS Logic Seminar

4/2/2020 23:49:27

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 8 April 2020, 17:00 hrs Zoom: Meeting URL is https://nus-sg.zoom.us/j/786053022 and Meeting ID is 786 053 022. Host: Frank Stephan, Department of Mathematics, NUS Speaker: Wu Guohua. Title: Members of thin Pi01 classes and their Turing degrees Abstract: Martin and Pour-El constructed in 1970 a consistent r.e. theory with few r.e. extensions. Motivated by this work, Cenzer, Downey, Jockusch and Shore raised the notion of thin Pi01 classes in their paper in 1993, where a Pi01 class P is thin if every Pi01 subclass of P is the intersection of P and some clopen set. While they put focus on various Turing degrees of members in these classes, they also constructed degrees below 0', one r.e., and one minimal, containing no members of any thin Pi01 classes. In this talk, I will present basic ideas of the constructions and provide some recent progress along this topic. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Set theory seminar this Friday: Iván Ongay Valverde

Toronto Set Theory Seminar

3/31/2020 16:14:47

Hi everyone,

Our seminar returns to break up your social isolation. This week, Iván Ongay Valverde from the University of Wisconsin will speak about Splitting localization and prediction numbers.

Abstract: In 1993, Newelski and Roslanowski studied some cardinal characteristics related to the unsymmetric game (I, as Geschke, called them the localization numbers). While doing this, they found the n-localization property. When a forcing has this property, you can ensure that all new reals are 'tame' somehow (for example, you do not add Cohen or Random reals).

In a different line of study, Andreas Blass worked with some cardinal characteristics related to the idea of guessing correctly a real number given certain amount of information (he called them evasion and prediction numbers). In 2010, it was an open question whether some possible variations of these numbers were known cardinal characteristics or not.

Impressively, these two notions are related.

In this talk, we will show that the k global adaptive prediction numbers are not any other cardinal characteristic. In particular, they are not the localization numbers. To do this, we will use techniques analogue to Newelski and Roslanowski and we will show that the n-localization can be weakened to get their result.

3/16/2020 10:53:45

Hi everyone,

This week, Ming Xiao will give the seminar. His talk is entitled The Borel chain conditions.

Abstract: In this talk, I will present some examples of Borel posets and show that the hierarchy of partition conditions proposed by Horn and Tarski ( $\sigma$ -finite chain condition, $\sigma$ -bounded chain condition, etc.), when requiring the pieces of partition to be Borel, is still distinct.

IMPORTANT: The seminar will be held remotely using the Zoom software during the usual time, Friday from 1:30 to 3:00 EDT. If you are interested in participating in the seminar and currently NOT a member of the mailing list (e.g., from Set Theory Talks) please send me an email to receive more information about how to join the meeting.

Stay safe,

Bill Chen

Wednesday seminar

Prague Set Theory Seminar

3/16/2020 3:25:18

Dear all, There is no seminar this week (Wednesday March 18th) due to the quarantine. The decision and announcement about the next seminar will be made/sent in about a week. Best, David

Logic Seminar 18 March 2020 17:00 hrs at NUS

NUS Logic Seminar

3/14/2020 23:48:12

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 18 March 2020, 17:00 hrs Room: S17#04-06, Department of Mathematics, NUS Speaker: Borisa Kuzeljevic. Title: Cofinal types on the the second uncountable cardinal. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html In the talk we will present some basic results about the Tukey ordering of the class of all directed sets whose cofinality is the second uncountable cardinal. We will isolate some basic directed sets in this class, and then show which of them have immediate successors in this ordering. This is a joint work with Stevo Todorcevic.

This Week in Logic at CUNY

3/12/2020 22:10:46

Hi everyone,

So far as we know, all seminars are on hiatus for an indefinite period, due to concerns about the covid-19 situation. Regular mailings of This Week in Logic are suspended for the time being, although special announcements will be sent as needed.

Take care of yourselves and each other,

Jonas

Set theory seminar this Friday: Jeffrey Bergfalk

Toronto Set Theory Seminar

3/11/2020 10:34:26

Hi everyone,

This week, Jeffrey Bergfalk from UNAM (Morelia) will speak on Definable (co)homology, topological rigidity, and problems of classification.

Abstract: We describe recent work, joint with Martino Lupini and Aristotelis Panagiotopoulos, at the interface of descriptive set theory and algebraic topology. This work begins with a consideration of the topologies arising naturally in the course of homology and cohomology computations. Our analysis of these topologies has two main benefits:

1. It affords us characterizations of the Borel complexity of several well-studied classification problems in mathematics, and
2. It yields refinements of classical homological and cohomological invariants which are valuable in their own right for the study of topological spaces.

We term the framework of these refined invariants definable (co)homology; this framework amounts to a retention of the descriptive set-theoretic information inhering in algebraic topology computations. These invariants are strong enough to imply several topological rigidity results concerning solenoids (of any dimension) and maps thereon. We will also show that techniques from algebraic topology can, reciprocally, extend the reach of descriptive set theory, by bounding, and in some cases precisely determining, the Borel complexity of classification problems concerning C*- algebras, their automorphisms, or Hermitian line bundles.

The talk will be held on Friday, March 13 in Fields 210 at 1:30 pm. If you will attend, please register using the following link:

Thanks,

Bill Chen

This Week in Logic at CUNY

3/8/2020 22:09:13

This Week in Logic at CUNY:

- - - - Monday, Mar 9, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, March 9, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Antonella Mallozzi (Providence College).
Title: Is There an Absolute Modality?

Abstract: Modality seems distinctively pluralistic: there are many kinds of possibility and necessity (logical, physical, metaphysical, normative, etc.), which seem significantly different from one another. However, the various modalities also seem to have much in common–perhaps simply in virtue of being kinds of modality. Should we suppose that there is some fundamental modality, one to which all the other modalities can be somehow reduced? Modal Monism says yes. Particularly, monists may treat the different modalities as relative to some absolute modality. However, Monism, reductionism, and absolute modality need not be a package. Specifically, the claim that some modality is absolute can be understood in ways which are independent of Monism and reductionism. In this talk, I raise concerns for monistic and reductionist programs in modal metaphysics, while also arguing that the notion of absolute modality is ambiguous. Depending on the framework, it means different things and captures quite different desiderata. After exploring several ways of disambiguating it, I suggest that while we possess and deploy a concept of absolute modality, that may be empty; or, otherwise put, no modal truth has the property of being “absolute”. I propose a pluralistic picture that still treats the different modalities as relative, while avoiding both absolute modality and reductionism. Importantly, the proposal won’t impact the philosophical significance of metaphysical modality.

- - - - Tuesday, Mar 10, 2020 - - - -

- - - - Wednesday, Mar 11, 2020 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: Tai-Danae Bradley, The Graduate Center, CUNY.
Date and Time: Wednesday March 11, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Modeling Probability Distributions as Quantum States.

Abstract: This talk features a passage from classical probability to quantum probability. The quantum version of a classical probability distribution is a density operator on a Hilbert space. The quantum version of a marginal probability distribution is a reduced density operator, and the operation that plays the role of marginalization is the partial trace. In particular, every joint probability distribution on a finite set can be modeling as a rank 1 density operator—a pure quantum state. With the partial trace, we recover the classical marginal probabilities, but we also uncover additional information. This extra information can be understood explicitly from the spectral information of the reduced density operators. I’ll describe these ideas and share how they contribute to understanding mathematical structure within natural language.

- - - - Thursday, Mar 12, 2020 - - - -

- - - - Friday, Mar 13, 2020 - - - -

Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, March 13, 12:30-2:00pm

Rebecca Coulson, United States Military Academy
TBA

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, March 13, 2:00-3:30pm

Chris Conidis, CUNY
The complexity of radical constructions in rings and modules

We present two different elementary algebraic constructions that are as complicated as possible and whose complexity vastly exceeds those typically found in the elementary algebra literature. The first is the prime radical of a noncommutative ring, while the second is the radical of a module. These constructions contrast similar constructions in more familiar contexts that we will also mention along the way. We will spend most of our time describing how to construct radicals that are as complicated as possible from a computability point of view.

Next Week in Logic at CUNY:

- - - - Monday, Mar 16, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, March 16, 4.15-6.15
Place: Room 7395, CUNY Graduate Center

David Papineau (CUNY)
Title: The Statistical Nature of Causation

Abstract: For over a hundred years econometricians, epidemiologists, educational sociologists and other non-experimental scientists have used asymmetric correlational patterns to infer directed causal structures. It is odd, to say the least, that no philosophical theories of causation cast any light on why these techniques work. Why do the directed causal structures line up with the asymmetric correlational patterns? Judea Pearl says that the correspondence is a “gift from the gods”. Metaphysics owes us a better answer. I shall attempt to sketch the outline of one.

- - - - Tuesday, Mar 17, 2020 - - - -

- - - - Wednesday, Mar 18, 2020 - - - -

- - - - Thursday, Mar 19, 2020 - - - -

- - - - Friday, Mar 20, 2020 - - - -

Ad Hoc Workshop on the Semantic Paradoxes
When? Friday March 20, Noon-5pm
Where? CUNY Graduate Center, room TBA
Who?
Will Nava, NYU, ‘Expressability and the (Un)Paradoxicality Paradoxes’
Brian Porter, GC, ‘Paraconsistent and Paracomplete Solutions to the Validity Curry Paradox’
Chris Scambler, NYU, ‘Metainferences and Paradox’
Open to? All interested
Queries? Graham Priest, priest.graham@gmail.com
The workshop is sponsored by the Kripke Center.

- - - - Other Logic News - - - -

MAMLS Spring Fling
This is a three day conference (April 22-24) in the mathematical field of set theory to be held at the CUNY Graduate Center. Consult the website (https://nylogic.github.io/MAMLSSpringFling/home.html) for more details.

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Logic Seminar Wed 11 March 2020 17:00 hrs at NUS by Thilo Weinert

NUS Logic Seminar

3/8/2020 18:24:12

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 11 March 2020, 17:00 hrs Room: S17#04-06, Department of Mathematics, NUS Speaker: Thilo Weinert, NUS Title: Polarised partition relation for order types URL: https://arxiv.org/abs/1810.13316 and https://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: We analyse partitions of products with two ordered factors in two classes where both factors are countable or well-ordered and at least one of them is countable. This relates the partition properties of these products to cardinal characteristics of the continuum. We build on work by Erdoes, Garti, Jones, Orr, Rado, Shelah and Szemeredi. In particular, we show that a theorem of Jones extends from the natural numbers to the rational ones but consistently extends only to three further equimorphism classes of countable orderings. This is made possible by applying a thirteen-year old theorem of Orr about embedding a given order into a sum of finite orders indexed over the given order. This is joint work with Lukas Klausner

Fulgencio Lopez, Uncountable equilateral sets and anti-Ramsey families of functions.

IMPAN Working Group in Applications of Set Theory

3/7/2020 13:45:59

Seminar: Working group in applications of set theory, IMPAN Tuesday, 10.03.2020, 10:15 pm, room 105, IMPAN, Śniadeckich 8, Warsaw. Speaker: Fulgencio Lopez (IMPAN) Title: "Uncountable equilateral sets and anti-Ramsey families of functions." Abstact: "The study of equilateral and separated sets in Banach spaces has been an active area of interest since Petty considered this question in non euclidean spaces in 1971. We will give some background results in the area and then focus on the case of spaces of continuous functions. In particular we will show that having an anti-Ramsey family of functions implies there is a compact connected K, such that its space of continuous functions has no uncountable equilateral sets. A known result says that the existence of uncountable equilateral sets in all nonseparable C(K) spaces is undecidable." (joint work with P. Koszmider) Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/ Cheers, Piotr.

Set theory seminar this Friday

Toronto Set Theory Seminar

3/4/2020 11:12:37

Hi everyone,

Hossein will speak in the seminar this week. His talk is entitled Rigidity of Souslin trees and $\diamondsuit$ .

Abstract:

We will show that $\diamondsuit$ is consistent with the statement there is no minimal Souslin tree. This answers a question due to Baumgartner. We will also show that there is a Souslin tree $T$ whose restriction on any $C \subset \omega_1$ is rigid and forcing with $T$ makes $T$ a Kurepa tree. This answers a question due to Gunter Fuchs.

The talk will be held on Friday, March 6 in Fields 210 at 1:30 pm. The talk is expected to be short, probably less than an hour in duration. If you will attend, please register using the following link:

http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Thanks,

Bill Chen

This Week in Logic at CUNY

3/1/2020 21:30:00

This Week in Logic at CUNY:

- - - - Monday, Mar 2, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, March 2, 4.15-6.15
Place: Room 7395, CUNY Graduate Center

Alex Citkin (Metropolitan Telecommunications).
Title: Deductive Systems with Unified Multiple-Conclusion Rules

Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.

- - - - Tuesday, Mar 3, 2020 - - - -

- - - - Wednesday, Mar 4, 2020 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: Noah Chrein, University of Maryland.
Date and Time: Wednesday March 4, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Hierarchy and Anisotropy in Categorical Ontology.

Abstract: The theory of sheaves on a site allows us to break down objects into local pieces and recover data about the global object. We wish to treat systems outside of mathematics in the same way: by breaking down objects into local pieces, analyzing the local pieces, and recombining to get an analysis of the whole. When running a simulation, it's not always relevant to understand the atoms of every object, sometimes it is enough to understand objects abstractly, this is the concept of "anisotropy". We propose a modeling scheme that follows the development of sheaf theory, and adds a notion of hierarchical anisotropy. Namely, instead of a covering in a site, {U_i -> X}, we will treat the U_i and X in two different categories, with "Ontological Expansions" O(X) = {U_i}. In this way, we can decide to treat objects globally, or if we need more specific information, we can expand into local pieces. To this end we define a Hierarchical Ontology.

- - - - Thursday, Mar 5, 2020 - - - -

- - - - Friday, Mar 6, 2020 - - - -

Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, March 6, 12:30-2:00pm

Dave Marker, McMaster University
Computability of the countable saturated differentially closed field

It's been known since work of Harrington in the early 1970s that computable differential fields have computable differential closures. Recently Calvert, Frolov, Harizanov, Knight, McCoy, Soskova, and Vatev showed that the countable saturated differentially closed field is computable. Their proof involves first creating an effective listing of all types and then using a result of Morley's on existence of computable saturated models. I will give a significant simplification of the enumeration result and, for completeness, sketch Morley's priority construction of a saturated model. Pillay has also given an alternative enumeration argument though ours seems more robust and generalizes to quantifier free types in ACFA.

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, March 6, 2:00-3:30pm
Johanna Franklin, Hofstra University
Lowness for isomorphism and Turing degrees

A Turing degree is low for isomorphism if whenever it can compute an isomorphism between two countably presented structures, there is already a computable isomorphism between them and thus there is no need to use the degree as an oracle at all. I will discuss the types of degrees that are low for isomorphism and the extent to which this class of degrees has the same properties as other lowness classes.

This work is joint with Reed Solomon.

Next Week in Logic at CUNY:

- - - - Monday, Mar 9, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, March 9, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Alex Citkin (Metropolitan Telecommunications).
Title: Deductive Systems with Unified Multiple-Conclusion Rules

Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.

- - - - Tuesday, Mar 10, 2020 - - - -

- - - - Wednesday, Mar 11, 2020 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: Tai-Danae Bradley, The Graduate Center, CUNY.
Date and Time: Wednesday March 11, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Modeling Probability Distributions as Quantum States.

Abstract: This talk features a passage from classical probability to quantum probability. The quantum version of a classical probability distribution is a density operator on a Hilbert space. The quantum version of a marginal probability distribution is a reduced density operator, and the operation that plays the role of marginalization is the partial trace. In particular, every joint probability distribution on a finite set can be modeling as a rank 1 density operator—a pure quantum state. With the partial trace, we recover the classical marginal probabilities, but we also uncover additional information. This extra information can be understood explicitly from the spectral information of the reduced density operators. I’ll describe these ideas and share how they contribute to understanding mathematical structure within natural language.

- - - - Thursday, Mar 12, 2020 - - - -

- - - - Friday, Mar 13, 2020 - - - -

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, March 13, 2:00-3:30pm

Chris Conidis, CUNY
TBA

- - - - Other Logic News - - - -

CONFERENCE ANNOUNCEMENT:

We are pleased to announce that the 2020 Boise Extravaganza in Set Theory (BEST) conference will take place in Ashland, Oregon, on the campus of Southern Oregon University, June 17–18, 2020.

https://www.boisestate.edu/math/best/
BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

2/29/2020 10:58:52

Dear all, There will be no seminar on Wednesday for the next two weeks (regular participants are unavailable). The seminar should meet again on Wednesday March 18th. Best, David

Tomasz Kochanek, On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0 II

IMPAN Working Group in Applications of Set Theory

2/29/2020 9:01:08

Seminar: Working group in applications of set theory, IMPAN TUESDAY, 3.03.2020, Seminar at 10:15 pm, room 105, IMPAN, Śniadeckich 8, Warsaw. Speaker: Tomasz Kochanek (IM PAN/MIM UW) Title: " On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0 II " Abstact: "Continuing our study of the poset of projections of the Calkin algebra Q(H), we will first show that below any strictly decreasing sequence of projections of Q(H) there is some nonzero projection. This fact gives rise to considering a `quantized` analogue of the pseudointersection number. Next, we will prove a general result saying that the poset of projections of Q(A) does not form a lattice, whenever Q(A) is the corona algebra of any stabilization A of some unital C*-algebra. In particular, this implies that the Calkin algebra is not an AW*-algebra. Then, we will proceed to the problem of representation of Q(H), focusing on two papers. First, Anderson and Bunce (Amer. J. Math. 1977) showed that under Martin's axiom (as well as under the Continuum Hypothesis), there exists a faithful *-representation of Q(H) such that the WOT-closure of its range is a II∞ type factor. Later, Anderson (J. Funct. Anal. 1979) showed that such a result holds true in ZFC. We shall discuss both of those (quite similar) constructions.". Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/ Cheers, Piotr.

(KGRC) research seminar talk on Thursday, March 5

Kurt Godel Research Center

2/27/2020 15:32:02

The KGRC welcomes as guests: Jana Marikova (host: Benjamin Miller) will stay until June 30. Clifton Ealy (host: Benjamin Miller) will visit from March 7 to March 15 and from May 9 to June 30. Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30 and give a talk on January 23. Jerzy Kakol (host: Damian Sobota) will stay from March 29 to April 4 and give a talk on April 2. Chi Tat Chong (host: Sy-David Friedman) will stay from June 17 to June 19 and give a talk on June 18. (Note: Professor Zeman's visit in the first week of March had to be canceled.) * * * Research seminar Kurt Gödel Research Center Thursday, March 5 "$\Pi_1^1$-subcompactness and type omission" Yair Hayut (KGRC) Strongly compact cardinals can be characterized in various ways: compactness of $L_{\kappa,\kappa}$, filter extensions, the existence of fine measures, the strong tree property (+inaccessibility) and many other ways. Localizations of those definitions produce a rich hierarchy. Supercompact cardinals have much fewer parallel characterizations, obtained typically by adding a normality assumption. In this talk I will present a characterization of supercompact cardinals in terms of compactness of $L_{\kappa,\kappa}$ with type omission. Using it, I will present a variant of the strong tree property which is (locally) weaker than the ineffable tree property and together with inaccessibility characterize supercompactness. Those characterizations localize to a characterization of $\Pi^1_1$-subcomapctness. This is a joint work with Menachem Magidor. Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien

Set Theory Seminar this Friday

Toronto Set Theory Seminar

2/26/2020 11:38:54

We will continue with the second part of the talk this Friday, February 28 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:

http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Bill Chen

On Wed, Feb 12, 2020 at 10:00 AM Bill Chen <chenwb@gmail.com> wrote:

Hi everyone,

I will talk this week about selectivity properties of spaces.

Abstract: This talk addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. This theory is concerned with the following general question about topological spaces: when does a map from $X$ into the hyperspace of closed nonempty subsets of $Y$ admit a continuous selection $X\to Y$ ?

We construct a space which is $L$ -selective but not $\mathbb{Q}$ -selective from $\mathfrak{d}=\aleph_1$ , and an $L$ -selective space which is not selective for a $P$ -point ultrafilter from CH. We also produce ZFC examples of Fréchet spaces where countable subsets are first countable which are not $L$ -selective. All of the notions will be defined in the talk, joint work with Paul Szeptycki.

The talk will be held at the usual time and place on Friday, February 14 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Thanks,
Bill Chen

Fernando Javier Núñez Rosales: Teoría descriptiva de grupos polacos no arquimedianos de transformaciones

Mexico City Logic Seminar

2/25/2020 11:52:00

Los grupos polacos no arquimedianos se pueden realizar como grupos de automorfismos de estructuras de Fraïssé. El objetivo de esta plática es revisar algunos fenómenos de la dinámica de estos grupos, los cuales pueden ser estudiados a través de propiedades combinatorias de clases de estructuras finitas o sistemas asociados a estas vía teoría de Fraïssé. Algunos de los tópicos centrales serán la extrema promediabilidad; el cómputo de flujos minimales universales; la existencia de simetrías genéricas y de genéricos enormes; aproximación por compactos; turbulencia; entre otras. Estos tópicos serán ilustrados con ejemplos.

Tagged: Fernando Javier Núñez Rosales

Logic Seminar 4 March 2020 17:00 hrs at NUS by Andre Nies

NUS Logic Seminar

2/24/2020 21:20:21

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 4 March 2019, 17:00 hrs Room: S17#04-06, Department of Mathematics, NUS Speaker: Andre Nies, University of Auckland Title: Analogs of combinatorial cardinal characteristics in computability theory URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: Our basic objects are infinite sets of natural numbers. In set theory, the MAD number is the least cardinality of a maximal almost disjoint class of sets of natural numbers. The ultrafilter number is the least size of an ultrafilter base. We study computability theoretic analogs of these cardinals. In our approach, all the basic objects will be infinite computable sets. A class of such basic objects is encoded as the set of columns of a set R, which allows us to study the Turing complexity of the class. We show that each non-low oracle computes a MAD class R, give a finitary construction of a c.e. MAD set (compatible with permitting), and on the other hand show that a 1-generic below the halting problem does not compute a MAD class. We show that the Turing degrees of ultrafilter bases are precisely the high degrees. Joint work with: Steffen Lempp, Joseph S. Miller and Mariya Soskova Reference: Section 8 of Logic Blog 2019 on Andre's homepage; soon also available as technical report on http://www.arxiv.org/.

SPECIAL ANNOUNCEMENT - This Week in Logic at CUNY - Two add'l talks today

This Week in Logic at CUNY

2/24/2020 12:35:59

Hi everyone,

Please see the announcement below, provided by Dennis Sullivan.

Best,

Jonas

---------------------------------

Prof. Francisco Javier Torres de Lizaur from Spain will give two talks today at the Einstein Chair seminar today, February 24, 2020:

The first will relate to geometry.

The second will relate to 3D fluid solutions in space to logic, computer science and PDE.

Namely, at 4:00p in logic knowing if a point enters a region contains the halting problem.

This affects PDE, analysis and computer science and at 2:00p finding links knots and foliations in stationary solutions of Euler’s fluid PDE in 3D.

<2:00p to tea then 4:00 to 5:00p>

This Week in Logic at CUNY

2/23/2020 20:33:37

This Week in Logic at CUNY:

- - - - Monday, Feb 24, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, February 24, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Dongwoo Kim (CUNY)
Title: A Truthmaker Semantics for Modal Logics

Abstract: This paper attempts to provide an exact truthmaker semantics for a family of normal modal propositional logic. The new semantics can be regarded as an “exactification” of the Kripke semantics in the sense of Fine (2014). For it offers an account of the accessibility relation on worlds in terms of the banning and allowing relations on states. The main idea is that an exact truthmaker for “Necessarily P” is a state that bans the exact falsifiers of P from obtaining, and an exact truthmaker for “Possibly P” is a state that allows the exact verifiers of P to obtain.

- - - - Tuesday, Feb 25, 2020 - - - -

- - - - Wednesday, Feb 26, 2020 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Noson S. Yanofsky, Brooklyn College, CUNY.
Date and Time: Wednesday February 26, 2020, 7:00 - 8:30 PM., Room 6417.

Title: Higher-Order Categorical Logic: From Section 1.7 and on.

Abstract: We will be talking about Polynomial categories and Kleisli categories of cotriples. We will also talk about coproducts in Cartesian closed categories and natural number objects.

- - - - Thursday, Feb 27, 2020 - - - -

- - - - Friday, Feb 28, 2020 - - - -

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 28, 2:00-3:30pm

Joel Nagloo, CUNY
TBA

Next Week in Logic at CUNY:

- - - - Monday, Mar 2, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, March 2, 4.15-6.15
Place: Room 7395, CUNY Graduate Center

Alex Citkin (Metropolitan Telecommunications).
Title: Deductive Systems with Unified Multiple-Conclusion Rules

Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.

- - - - Tuesday, Mar 3, 2020 - - - -

- - - - Wednesday, Mar 4, 2020 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: Noah Chrein, University of Maryland.
Date and Time: Wednesday March 4, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Hierarchy and Anisotropy in Categorical Ontology.

Abstract: The theory of sheaves on a site allows us to break down objects into local pieces and recover data about the global object. We wish to treat systems outside of mathematics in the same way: by breaking down objects into local pieces, analyzing the local pieces, and recombining to get an analysis of the whole. When running a simulation, it's not always relevant to understand the atoms of every object, sometimes it is enough to understand objects abstractly, this is the concept of "anisotropy". We propose a modeling scheme that follows the development of sheaf theory, and adds a notion of hierarchical anisotropy. Namely, instead of a covering in a site, {U_i -> X}, we will treat the U_i and X in two different categories, with "Ontological Expansions" O(X) = {U_i}. In this way, we can decide to treat objects globally, or if we need more specific information, we can expand into local pieces. To this end we define a Hierarchical Ontology.

- - - - Thursday, Mar 5, 2020 - - - -

- - - - Friday, Mar 6, 2020 - - - -

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, March 6, 2:00-3:30pm
Johanna Franklin, Hofstra University
Lowness for isomorphism and Turing degrees

A Turing degree is low for isomorphism if whenever it can compute an isomorphism between two countably presented structures, there is already a computable isomorphism between them and thus there is no need to use the degree as an oracle at all. I will discuss the types of degrees that are low for isomorphism and the extent to which this class of degrees has the same properties as other lowness classes.

This work is joint with Reed Solomon.

- - - - Other Logic News - - - -

CONFERENCE ANNOUNCEMENT:

We are pleased to announce that the 2020 Boise Extravaganza in Set Theory (BEST) conference will take place in Ashland, Oregon, on the campus of Southern Oregon University, June 17–18, 2020.

https://www.boisestate.edu/math/best/
BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Tomasz Kochanek, On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0

IMPAN Working Group in Applications of Set Theory

2/22/2020 9:39:21

Seminar: Working group in applications of set theory, IMPAN Note the change from Thursdays to Tuesdays and afternoons to mornings. TUESDAY, 25.02.2020, Seminar at 10:15 pm, room 105, IMPAN, Śniadeckich 8, Warsaw. Speaker: Tomasz Kochanek (IM PAN/MIM UW) Title: " On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0" Abstact: "The first part will be a mild introduction to the Calkin algebra Q(H) which was first investigated thoroughly by J.W. Calkin in his paper published in Annals Math. in 1941. We shall present some basic facts on Q(H), explaining what it has to do with essential spectra, Fredholm operators, the BDF theory of extensions, and a few other things. With the aid of Banach limit, we will construct a `concrete' representation ρ of Q(H) on a Hilbert space of density continuum. Also, we will show that the range of ρ is not closed in the weak operator topology, which should provoke considering the problem of finding some `special' representations of Q(H), as well as the problem of extending *-homomorphisms into Q(H). This will be the topic of the second part". Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/ Cheers, Piotr.

Wednesday seminar

Prague Set Theory Seminar

2/21/2020 12:39:39

Dear all, The seminar meets on Wednesday February 26th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Egbert Thümmel will talk about the non-existence of ω1 purely injective ideals in Boolean algebras. Best, David

This Week in Logic at CUNY

2/18/2020 22:30:32

This Week in Logic at CUNY:

- - - - Monday, Feb 17, 2020 - - - -

- - - - Tuesday, Feb 18, 2020 - - - -

- - - - Wednesday, Feb 19, 2020 - - - -

MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, February 19, 6:30-8:00pm

James Geiser
Soundness and the Gödel Undecidability Theorem

The goal of Gödel’s argument that the theory (T) of Peano Arithmetic is not complete, was to show that the Gödel sentences, GG , and it’s negation, are not provable in T, unless T is inconsistent. In this paper we examine the first half of this argument, namely, that from a hypothetical derivation, PGPG, of GG, a derivation, PfPf, can be constructed that ends in a contradiction. We make the observation that the Gödel argument depends on the metatheory concept of representability that, in turn, depends on the metatheory concept of soundness. Our analysis leads to two main observations, the first well know, and the second, a challenge to the standard undecidability argument.

1 – The existence of PGPG implies that T is unsound. This conclusion does not require the further construction, from PGPG, of the derivation PfPf.

2 - We argue that effectuation of the construction of PfPf is obstructed, because that effectuation requires acceptance of a contradiction in the metatheory regarding the soundness of T.

This is joint work with Catherine Hennix.

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday February 19, 2020, 7:00 - 8:30 PM., Room 6417.
Speaker: Todd Trimble, Western Connecticut State University.
Title: The Universal Property of the Bar Construction.

Abstract: The bar construction is a fundamental construction used throughout homological algebra and algebraic topology, including for example the construction of classifying bundles, deloopings of suitable H-spaces, and free resolutions of general algebras and the cohomology thereof. The underlying theme is that the bar construction produces canonical contractible or acyclic simplicial algebras, as usually explained by the acyclic models theorem. In this talk we sharpen this result, giving a precise sense in which the bar construction is a universal acyclic simplicial algebra, here recasting "acyclic" not as a property but as an algebraic structure, whereby acyclic structures are coalgebras over the decalage comonad.

- - - - Thursday, Feb 20, 2020 - - - -

- - - - Friday, Feb 21, 2020 - - - -

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 21, 2:00-3:30pm
Andrey Morozov, Novosibirsk State University
On ΣΣ-preorderings in HF(R)
We prove that ω1ω1 cannot be embedded into any preordering ΣΣ-definable with parameters in the hereditarily finite superstructure over the ordered field of real numbers, HF(R). As corollaries, we obtain characterizations of ΣΣ-presentable ordinals and Gödel constructive sets of kind LαLα. It also follows that there are no ΣΣ-presentations for structures of TT-, mm-, 11-, and tttt-degrees over HF(R).

Next Week in Logic at CUNY:

- - - - Monday, Feb 24, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, February 24, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Dongwoo Kim (CUNY)
Title: A Truthmaker Semantics for Modal Logics

Abstract: This paper attempts to provide an exact truthmaker semantics for a family of normal modal propositional logic. The new semantics can be regarded as an “exactification” of the Kripke semantics in the sense of Fine (2014). For it offers an account of the accessibility relation on worlds in terms of the banning and allowing relations on states. The main idea is that an exact truthmaker for “Necessarily P” is a state that bans the exact falsifiers of P from obtaining, and an exact truthmaker for “Possibly P” is a state that allows the exact verifiers of P to obtain.

- - - - Tuesday, Feb 25, 2020 - - - -

- - - - Wednesday, Feb 26, 2020 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday February 26, 2020, 7:00 - 8:30 PM., Room 6417.

Title: Higher-Order Categorical Logic: From Section 1.7 and on.

Abstract: We will be talking about Polynomial categories and Kleisli categories of cotriples. We will also talk about coproducts in Cartesian closed categories and natural number objects.

- - - - Thursday, Feb 27, 2020 - - - -

- - - - Friday, Feb 28, 2020 - - - -

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 28, 2:00-3:30pm

Joel Nagloo, CUNY
TBA

- - - - Other Logic News - - - -

CONFERENCE ANNOUNCEMENT:

We are pleased to announce that the 2020 Boise Extravaganza in Set Theory (BEST) conference will take place in Ashland, Oregon, on the campus of Southern Oregon University, June 17–18, 2020.

https://www.boisestate.edu/math/best/
BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Logic seminar this week cancelled

NUS Logic Seminar

2/18/2020 1:36:05

Hello, I just want to inform you that our speaker for the logic seminar this week is ill and on mc until Thursday. Therefore there is no logic seminar this week. My apologies and all the best wishes to Thilo for his health. Best regards, Frank

Wednesday seminar

Prague Set Theory Seminar

2/13/2020 6:13:04

Dear all, There is no seminar next week, Wednesday February 19th. The seminar should meet again on Wednesday February 26th. Best, David

Logic Seminar 19 Feb 2020 17:00 hrs at NUS

NUS Logic Seminar

2/13/2020 2:47:21

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 19 February 2019, 17:00 hrs Room: S17#04-06, Department of Mathematics, NUS Speaker: Thilo Weinert, NUS Title: Polarised partition relation for order types URL: https://arxiv.org/abs/1810.13316 and https://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: We analyse partitions of products with two ordered factors in two classes where both factors are countable or well-ordered and at least one of them is countable. This relates the partition properties of these products to cardinal characteristics of the continuum. We build on work by Erdoes, Garti, Jones, Orr, Rado, Shelah and Szemeredi. In particular, we show that a theorem of Jones extends from the natural numbers to the rational ones but consistently extends only to three further equimorphism classes of countable orderings. This is made possible by applying a thirteen-year old theorem of Orr about embedding a given order into a sum of finite orders indexed over the given order. This is joint work with Lukas Klausner

Set Theory Seminar this Friday

Toronto Set Theory Seminar

2/12/2020 10:00:00

Hi everyone,

I will talk this week about selectivity properties of spaces.

Abstract: This talk addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. This theory is concerned with the following general question about topological spaces: when does a map from $X$ into the hyperspace of closed nonempty subsets of $Y$ admit a continuous selection $X\to Y$ ?

We construct a space which is $L$ -selective but not $\mathbb{Q}$ -selective from $\mathfrak{d}=\aleph_1$ , and an $L$ -selective space which is not selective for a $P$ -point ultrafilter from CH. We also produce ZFC examples of Fréchet spaces where countable subsets are first countable which are not $L$ -selective. All of the notions will be defined in the talk, joint work with Paul Szeptycki.

The talk will be held at the usual time and place on Friday, February 14 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:

http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Thanks,

Bill Chen

Boise Extravaganza in Set Theory, Ashland, OR, June 17-18, 2020

Conference

2/12

We are pleased to announce that the 2020 Boise Extravaganza in Set Theory will take place in Ashland, Oregon, on the campus of Southern Oregon University, during June 17–18. BEST is an international conference featuring talks on a broad range of recent advances in research in set theory and related fields. Researchers from all areas of logic are welcome. BEST particularly aims to support the careers of young researchers in set theory and logic. The conference is organized by the Set Theory group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division. Site: https://www.boisestate.edu/math/best/ Contact: best@boisestate.edu Organizers: Liljana Babinkostova (Boise State University), John Clemens (Boise State University), Samuel Coskey (Boise State University), Marion Scheepers (Boise State University) Scientific support Natasha Dobrinen (University of Denver) Plenary speakers: * David Fernández-Bretón (Universidad Nacional Autónoma de México) * Victoria Gitman (CUNY Graduate Center) * Jun Le Goh (University of Wisconsin) * Lynne Yengulalp (University of Dayton and Wake Forest University) * Joseph Zielinski * … more to come! The NSF supports travel grants for student and postdoctoral speakers at BEST. (If you are in another category and could use funding, let us know as well.) We strongly encourage members of groups underrepresented in mathematics to apply! Please visit the conference web site for application instructions.

Tagged: David Fernández-Bretón, Jun Le Goh, Lynne Yengulalp, Joseph Zielinski, Victoria Gitman

Ultrafilters and Ultraproducts Across Mathematics, Pisa, Italy, May 31-June 6, 2020

Conference

2/11/2020

ULTRAMATH 2020 Ultrafilters and Ultraproducts Across Mathematics and Related Topics May 31 - June 6, 2020, Pisa, Italy http://people.dm.unipi.it/ultramath2020/ Dear all, We are happy to announce the upcoming event "ULTRAMATH 2020 - Ultrafilters and Ultraproducts Across Mathematics and Related Topics", that will be held in Pisa (Italy) from May 31st to June 6th 2020. The international Conference "ULTRAMATH 2020” aims to present recent results in the whole spectrum of mathematics which are grounded on the use of ultrafilters and ultraproducts. Its main goals: • Disseminate information about the various techniques related to the use of ultrafilters and ultraproducts, and their potential to attack open problems. • Bring together researchers with different backgrounds, and encourage their collaborations and interactions, especially on topics connecting different areas of mathematics. The covered topics of UltraMath 2020 include (but are not limited to): • Additive and Combinatorial Number Theory. • Combinatorics and Ramsey Theory. • Algebra and Geometry. • General Topology. • Measure Theory. • Ergodic Theory and Dynamics. • Functional Analysis and Metric Spaces. • Nonstandard Analysis and Model Theory. • Generalized Spaces and Differential Equations. • Set Theory. Greater prominence will be given to those results that satisfy (most of) the following conditions: • The results can be formulated and presented in non-specialist terms, and be in principle understandable by any practicing mathematician. • The usage of ultrafilters/ultraproducts is important (or even essential) in obtaining these results. • The results connect different areas of mathematics. • The results reveal new facets of known important topics. This is the second edition of “UltraMath”, after the one held in Pisa in 2008: http://people.dm.unipi.it/ultramath. Scientific Committee: Vitaly Bergelson (Ohio State University, USA) Andreas Blass (University of Michigan, USA) Mauro Di Nasso (Università di Pisa, Italia) Renling Jin (College of Charleston, USA) Organizing Committee: Mauro Di Nasso (Università di Pisa, Italia) – chair Lorenzo Luperi Baglini (Università di Milano, Italia) LIST OF INVITED SPEAKERS Vieri Benci — Università di Pisa, Italia Vitaly Bergelson — Ohio State University, USA Andreas Blass — University of Michigan Ann Arbor, USA Artem Chernikov — University of California Los Angeles (UCLA), USA Natasha Dobrinen — University of Denver, USA Cornelia Druţu — University of Oxford, UK Victoria Gitman — City University of New York (CUNY), USA Isaac Goldbring — University of California Irvine (UCI), USA C. Ward Henson – University of Illinois Urbana-Champaign, USA Neil Hindman — Howard University, USA Michael Hrušák — Universidad Nacional Autónoma, México Renling Jin — College of Charleston, USA Steven Leth — University of Northern Colorado, USA Martino Lupini — Victoria University, New Zealand Joel Moreira — University of Warwick, UK Jaroslav Nešetřil — Charles University Praha, Czech Republic Florian Richter – Northwestern University, USA David A. Ross — University of Hawaii, USA Sławomir Solecki — Cornell University, USA Dona Strauss — University of Hull, UK Simon Thomas — Rutgers University, USA Stevo Todorcevic — Univ. of Toronto, Canada and Univ. Paris Diderot, France There will be a call for contributed papers. Moreover, depending on the funds available, participation of young researchers and researchers from disadvantages areas will be supported. You can preregister by sending an email to ultramath2020@cs.dm.unipi.it with your name and institution. Updated information about UltraMath 2020 will be posted on the website: http://people.dm.unipi.it/ultramath2020/. Those who need more information, can contact the organizers at: ultramath2020@cs.dm.unipi.it. We hope to see you in Pisa! Best regards, The Organizers

Tagged: Vieri Benci, Vitaly Bergelson, Andreas Blass, Artem Chernikov, Natasha Dobrinen, Cornelia Druţu, Victoria Gitman, Isaac Goldbring, C. Ward Henson, Neil Hindman, Michael Hrušák, Renling Jin, Steven Leth, Martino Lupini, Joel Moreira, Jaroslav Nešetřil, Florian Richter, David A. Ross, Sławomir Solecki, Dona Strauss, Simon Thomas, Stevo Todorcevic

Logic Colloquium, Poznań, Poladn, July 13-18, 2020

Conference

2/10/2020

Logic Colloquium 2020 Call for Papers July 13-18, 2020, Poznań, Poland https://lc2020.pl/ * The Logic Colloquium is the European Summer Meeting of the Association for Symbolic Logic, which in 2020 will be held from 13th to 18th of July at the Adam Mickiewicz University, Poznań, Poland. It is organized jointly by the AMU Faculties: of Psychology and Cognitive Science and of Mathematics and Computer Science. * Registration is now open. * Important dates: - March 31st, 2020 deadline for abstract submission - April 13th, 2020 deadline for student travel awards applications - April 30th, 2020 notifications - May 25th, 2020 camera-ready abstracts due - June 13th, 2020 early payments deadline - July 7th, 2020 late payments deadline * Goedel Lecture: Elisabeth Bouscaren (CNRS - Université Paris-Sud) * Tutorial Speakers: Krzysztof Krupiński (University of Wrocław), Andrew Marks (University of California Los Angeles) * Plenary Speakers: Linda Westrick (Pennsylvania State University), Benoit Monin (Créteil University), Noam Greenberg (Victoria University of Wellington), Vera Fischer (University of Viena), Luca Motto Ros (University of Turin), Elaine Pimentel (Federal University of Rio Grande do Norte), Frank Pfenning (Carnegie Mellon University), Johan van Benthem (University of Amsterdam), Ryan Williams (Massachusetts Institute of Technology), Artem Chernikov (University of California Los Angeles) * Detailed information can be found on the webpage.

Tagged: Elisabeth Bouscaren, Krzysztof Krupiński, Andrew Marks, Linda Westrick, Benoit Monin, Noam Greenberg, Vera Fischer, Luca Motto Ros, Elaine Pimentel, Frank Pfenning, Johan van Benthem, Ryan Williams, Artem Chernikov

This Week in Logic at CUNY

2/9/2020

This Week in Logic at CUNY:

- - - - Monday, Feb 10, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, February 10, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Melissa Fusco (Columbia)
Is Free Choice Cancellable?

I explore the implications of the Tense Phrase deletion operation known as sluicing (Ross 1969) for the semantic and pragmatic literature on the Free Choice effect (Kamp 1973, von Wright 1969). I argue that the time-honored ‘I don’t know which’-riders on Free Choice sentences, traditionally taken to show that the effect is pragmatic, are sensitive to scope. Careful attention to such riders suggests that these sluices do not show cancellation on Free Choice antecedents in which disjunction scopes narrower than the modal.

- - - - Tuesday, Feb 11, 2020 - - - -

- - - - Wednesday, Feb 12, 2020 - - - -

NO TALKS TODAY - LINCOLN'S BIRTHDAY

Today's New York City Category Theory Seminar talk by Tai-Danae Bradley has been rescheduled for March 11.

- - - - Thursday, Feb 13, 2020 - - - -

- - - - Friday, Feb 14, 2020 - - - -

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 14, 2:00-3:30pm

Bartosz Wcisło, University of Warsaw
Tarski boundary

Our talk concerns axiomatic theories of truth predicates. They are theories obtained by adding to Peano Arithmetic ( $P A$ ) a fresh predicate $T (x)$ with the intended reading ' $x$ is (a code of) a true sentence in the language of arithmetic' together with some axioms governing newly added predicate.

The canonical example of such a theory is $C T -$ (Compositional Truth). Its axioms state that the truth predicate is compositional. For instance, a conjunction is true iff both conjuncts are. If we add to $C T -$ full induction in the extended language, we call the resulting theory $C T$ .

It is easy to check that $C T$ is not conservative over $P A$ , i.e., it proves new arithmetical sentences. On the other hand, by a nontrivial theorem of Kotlarski, Krajewski, and Lachlan, $C T -$ extends $P A$ conservatively.

In our talk, we will discuss results on the strength of theories between $C T -$ and $C T$ . It turns out that the natural axioms concerning purely truth theoretic properties of the newly added predicate (as opposed to axiom schemes which are consequences of induction in more general context) are typically either conservative or exactly equal to $C T 0$ , the theory of compositional truth with $Δ 0$ -induction. Thus $C T 0$ turns out to be a surprisingly robust theory and, arguably, the minimal 'natural' non-conservative theory of truth.

Next Week in Logic at CUNY:

- - - - Monday, Feb 17, 2020 - - - -

- - - - Tuesday, Feb 18, 2020 - - - -

- - - - Wednesday, Feb 19, 2020 - - - -

MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, February 19, 6:30-8:00pm

James Geiser
Soundness and the Gödel Undecidability Theorem

The goal of Gödel’s argument that the theory (T) of Peano Arithmetic is not complete, was to show that the Gödel sentences, $G$ , and it’s negation, are not provable in T, unless T is inconsistent. In this paper we examine the first half of this argument, namely, that from a hypothetical derivation, $P G$ , of $G$ , a derivation, $P f$ , can be constructed that ends in a contradiction. We make the observation that the Gödel argument depends on the metatheory concept of representability that, in turn, depends on the metatheory concept of soundness. Our analysis leads to two main observations, the first well know, and the second, a challenge to the standard undecidability argument.

1 – The existence of $P G$ implies that T is unsound. This conclusion does not require the further construction, from $P G$ , of the derivation $P f$ .

2 - We argue that effectuation of the construction of $P f$ is obstructed, because that effectuation requires acceptance of a contradiction in the metatheory regarding the soundness of T.

This is joint work with Catherine Hennix.

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday February 19, 2020, 7:00 - 8:30 PM., Room 6417.
Speaker: Todd Trimble, Western Connecticut State University.
Title: The Universal Property of the Bar Construction.

Abstract: The bar construction is a fundamental construction used throughout homological algebra and algebraic topology, including for example the construction of classifying bundles, deloopings of suitable H-spaces, and free resolutions of general algebras and the cohomology thereof. The underlying theme is that the bar construction produces canonical contractible or acyclic simplicial algebras, as usually explained by the acyclic models theorem. In this talk we sharpen this result, giving a precise sense in which the bar construction is a universal acyclic simplicial algebra, here recasting "acyclic" not as a property but as an algebraic structure, whereby acyclic structures are coalgebras over the decalage comonad.

- - - - Thursday, Feb 20, 2020 - - - -

- - - - Friday, Feb 21, 2020 - - - -

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 21, 2:00-3:30pm
Andrey Morozov, Novosibirsk State University
On $Σ$ -preorderings in HF(R)
We prove that

ω 1

cannot be embedded into any preordering

Σ

-definable with parameters in the hereditarily finite superstructure over the ordered field of real numbers, HF(R). As corollaries, we obtain characterizations of

Σ

-presentable ordinals and Gödel constructive sets of kind

L α

. It also follows that there are no

Σ

-presentations for structures of

T

-,

m

-,

1

-, and

t t

-degrees over HF(R).

- - - - Other Logic News - - - -

CONFERENCE ANNOUNCEMENT:

The “Sao Paulo School of Advanced Science on Contemporary Logic, Rationality and Information - SPLogIC”, sponsored by FAPESP and promoted by the Centre for Logic, Epistemology and the History of Science (CLE) of the University of Campinas (Unicamp), Brazil, will be held at Unicamp from July 13th to 24th, 2020.

The School celebrates the 90th anniversary of Newton da Costa and aims at: providing an overview of the state-of-art methodology and research on contemporary logic (featuring non-classical logics), rationality, and information.

The program comprises 9 courses and 9 plenary talks delivered in English by experts in each topic, as well as oral presentations (LED Talks) and poster sessions by the students.

Topics to be covered include:

• History and Philosophy of Paraconsistent Logics

• The Australian, Belgian, Brazilian, and Israeli schools on paraconsistency

• Logic and Reasoning, Logic and Information, Logic and Argumentation

• Methodological aspects on interpreting, translating and combining logics

• Logic, Probability and Artificial Intelligence.

The event will select 100 fully-funded participants (50 grantees from all states of Brazil and 50 international grantees). Funding includes airfare, medical insurance, accommodation and meals throughout the two weeks.

Undergraduate students, graduate students and postdoctoral fellows (up to 5 years after completion of the Ph.D) from all countries are encouraged to apply.

Applications are open from January 15th to February 22th, 2020.

More information and Call for Applications at https://splogic.org.

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

2/7/2020

Dear all, The seminar meets on Wednesday February 12th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: The program is not yet determined, presumably either Jonathan Verner or I will talking about something. Best, David

Udine Workshop on Singular Cardinals, Udine, Italy, July 6-7, 2020

Conference

2/7/2020

Udine Workshop on Singular Cardinals We are happy to announce the upcoming "Udine Workshop on Singular Cardinals", that will be held in Udine (Italy) on 6-7 July 2020. It will be held at Palazzo di Toppo Wassermann, a prestigious 18th-century palace. Singular cardinals are transversal to set theory and beyond, and this will be an occasion to bring together researchers working on singular cardinals and share the latest developments on this topic. Organizers: Vincenzo Dimonte (University of Udine) Mirna Dzamonja (The University of East Anglia) Luca Motto Ros (University of Torino) Talks: James Cummings (Carnegie Mellon University) Péter Komjáth (Eötvös Loránd University) Menachem Magidor (The Hebrew University of Jerusalem) * Itay Neeman (UCLA) * Assaf Rinot (Bar-Ilan University) Jouko Väänänen (University of Helsinki) * To confirm Website: https://users.dimi.uniud.it/~vincenzo.dimonte/WSC2020.html There will be some slots open for contributed talks, and all the interested researchers and students are encouraged to apply. To propose a contributed talk, please write to vincenzo.dimonte@uniud.it by May the 31st. For further information, contact vincenzo.dimonte@uniud.it

http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Tagged: James Cummings, Péter Komjáth, Menachem Magidor, Itay Neeman, Assaf Rinot, Jouko Väänänen

(KGRC) research seminar talk on WEDNESDAY, February 12

Kurt Godel Research Center

2/6/2020

The KGRC welcomes as guests: Jana Marikova (host: Benjamin Miller) will stay until June 30. Clifton Ealy (host: Benjamin Miller) will visit from March 7 to March 15 and from May 9 to June 30. Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30. Vincenzo Dimonte (host: Sy-David Friedman) will stay from February 8 to February 13 and give a talk on February 12 (see below). Martin Zeman (hosts: Sandra Müller and Monroe Eskew) will visit end of February or early March (to be determined) and give a talk on March 5 (tentative date). Jerzy Kakol (host: Damian Sobota) will stay from March 29 to April 4 and give a talk on April 2. Chi Tat Chong (host: Sy-David Friedman) will stay from June 17 to June 19 and give a talk on June 18. * * * Research seminar Kurt Gödel Research Center WEDNESDAY, February 12 (Please note the unusual day.) "Regularity properties in singular generalized descriptive set theory" Vincenzo Dimonte (University of Udine, Italy) Generalized descriptive set theory is the study of definable subsets of the space ${}^\kappa 2$ with the bounded topology. Such study has been overwhelmingly focussed on the case with $\kappa$ regular. Motivated by the theory of rank-into-rank cardinals, we concentrated instead on the case of $\kappa$ singular of cofinality $\omega$, painting a picture that is quite similar to the classical descriptive set theory case. This talk is going to center around the generalization of regularity properties (Perfect Set Property and Baire Property) in this context. The PSP is still akin to the classical case, while the BP probably needs more large-cardinal power to be non-trivial. Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien

This Week in Logic at CUNY

2/3/2020

Hi everyone,

This is the first edition of "This Week in Logic" in this new semester and new decade - welcome back! Future mailings will occur weekly on Sunday evenings.

Best,

Jonas Reitz

This Week in Logic at CUNY:

- - - - Tuesday, Feb 4, 2020 - - - -

- - - - Wednesday, Feb 05, 2020 - - - -

MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, Feb 5, 6:30-8:00pm
Athar Abdul-Quader, Purchase College
The pentagon saga continues

I will continue to speak about Jim Schmerl's recent paper on the pentagon lattice

N 5

. In this talk, I will outline the main result that no model of PA has a 'mixed' elementary extension such that the resulting interstructure lattice is isomorphic to the pentagon.

- - - - Thursday, Feb 06, 2020 - - - -

- - - - Friday, Feb 07, 2020 - - - -

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, Feb 7, 2:00-3:30pm
Victor Selivanov, Institute of Informatics Systems, Novosibirsk
A Q-Wadge hierarchy in quasi-Polish spaces

The Wadge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). We extend it to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show that our extension behaves well in second countable spaces and especially in quasi-Polish spaces. In particular, all levels are preserved by continuous open surjections between second countable spaces, which implies, e.g., several Hausdorff-Kuratowski-type theorems in quasi-Polish spaces. In fact, many results hold not only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q.

Next Week in Logic at CUNY:

- - - - Monday, Feb 10, 2020 - - - -

Logic and Metaphysics Workshop
Date: Monday, February 10, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Melissa Fusco (Columbia).
Title: A Deontic Logic for Two Paradoxes of Deontic Modality

Abstract: In this paper, we take steps towards axiomatizing the two dimensional deontic logic in Fusco (2015), which validates a form of free choice permission (von Wright 1969, Kamp 1973; (1) below) and witnesses the nonentailment known as Ross’s Puzzle (Ross 1941; (2) below).

(1) You may have an apple or a pear ⇒ You may have an apple, and you may have a pear.
(2) You ought to post the letter = ̸⇒ You ought to post the letter or burn it.

Since <>(p or q) = (<>p ∨ <>q) and [ ](p) ⇒ [ ](p ∨ q) are valid in any normal modal logic – including standard deontic logic – the negations of (1)-(2) are entrenched in modal proof systems. To reverse them without explosion will entail excavating the foundations of the propositional tautologies. The resulting system pursues the intuition that classical tautologies involving disjunctions are truths of meaning, rather than propositional necessities. This marks a departure from the commitments the propositional fragment of a modal proof system is standardly taken to embody.

Note: This is joint work with Arc Kocurek (Cornell).

- - - - Tuesday, Feb 11, 2020 - - - -

- - - - Wednesday, Feb 12, 2020 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Tai-Danae Bradley, The Graduate Center, CUNY.
Date and Time: Wednesday February 12, 2020, 7:00 - 8:30 PM., Room 6417.
Title: TBA.
Abstract: TBA.

- - - - Thursday, Feb 13, 2020 - - - -

- - - - Friday, Feb 14, 2020 - - - -

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Set theory seminar this week: Assaf Shani

Toronto Set Theory Seminar

2/3/2020

Hi everyone,

This week Assaf Shani from Carnegie Mellon University will speak in the seminar. His talk is entitled "Borel reducibility and symmetric models."

Abstract: We develop a correspondence between Borel equivalence relations induced by closed subgroups of $S_\infty$ and symmetric models of set theory without choice, and apply it to prove a conjecture of Hjorth-Kechris-Louveau (1998). For example, we show that the equivalence relation $\cong^*_{\omega+1,0}$ is strictly below $\cong^*_{\omega+1,<\omega}$ in Borel reducibility. By results of Hjorth-Kechris-Louveau, $\cong^*_{\omega+1,<\omega}$ bounds the complexity of $\sigma^0_{\omega+1}$ actions of $S_\infty$ , while $\cong^*_{\omega+1,0}$ bounds the complexity of $\sigma^0_{\omega+1}$ actions of "well behaved'' closed subgroups of $S_\infty$ , such as abelian groups. The notions mentioned above will be defined in the talk, and I will also survey the results of Hjorth-Kechris-Louveau.

The talk will be held on Friday, February 7 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:

Thanks,

Bill Chen

Logic Seminar 12 Feb 2020 17:00 hrs at NUS

NUS Logic Seminar

2/3/2020

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 12 February 2020, 17:00 hrs Room: S17#04-06, Department of Mathematics, NUS Speaker: Ashutosh Kumar Title: On some problems in set-theoretic Eucildean Ramsey theory URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: We shall discuss some questions in Euclidean Ramsey theory where techniques from set theory have played a role.

Wednesday seminar

Prague Set Theory Seminar

1/30/2020

Dear all, The seminar meets on Wednesday February 5th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. We will have quests speakers from Morelia. The main program is: César Corral -- Frechet-like properties in almost disjoint families Abstract: We will study some strong Frechet properties and properties very related to the preservation of Frechetness under products. Our main tool to construct counterexamples to some implications between them will be the use of almost disjoint families. Time permitting, there might be more topics/speakers. Best, David

Tagged: César Corral

Logic Seminar

Barcelona Logic Seminar

1/29/2020 10:09:59

Next session of the Logic Seminar

Asaf Karagila

Newton International Fellow, School of Mathematics, UEA (Norwich)

THE POWER OF POWER SETS OF COUNTABLE UNIONS OF COUNTABLE SETS

Wednesday, February 5.
12:30
IMUB Lecture Room, Facultat de Matemàtiques i Informàtica, UB.

http://www.ub.edu/slb/Seminar.html

Aquest missatge, i els fitxers adjunts que hi pugui haver, pot contenir informació confidencial o protegida legalment i s’adreça exclusivament a la persona o entitat destinatària. Si no consteu com a destinatari final o no teniu l’encàrrec de rebre’l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si l’heu rebut per error, informeu-ne el remitent i elimineu del sistema tant el missatge com els fitxers adjunts que hi pugui haver.

Este mensaje, y los ficheros adjuntos que pueda incluir, puede contener información confidencial o legalmente protegida y está exclusivamente dirigido a la persona o entidad destinataria. Si usted no consta como destinatario final ni es la persona encargada de recibirlo, no está autorizado a leerlo, retenerlo, modificarlo, distribuirlo o copiarlo, ni a revelar su contenido. Si lo ha recibido por error, informe de ello al remitente y elimine del sistema tanto el mensaje como los ficheros adjuntos que pueda contener.

This email message and any attachments it carries may contain confidential or legally protected material and are intended solely for the individual or organization to whom they are addressed. If you are not the intended recipient of this message or the person responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any part of it. If you have received the message by mistake, please inform the sender of this and eliminate the message and any attachments it carries from your account.

Re: Set Theory Seminar

Barcelona Set Theory Seminar

1/24/2020

Dear Colleagues,

Please find attached the announcement of the next session of the Barcelona Set Theory seminar.

You are all welcome to attend.

Best regards,

Joan

Joan Bagaria 🎗

ICREA Research Professor

Universitat de Barcelona

Departament de Matemàtiques i Informàtica

Gran Via de les Corts Catalanes 585

08007 Barcelona

Catalonia

Phone: +34 93 402 1609

Eduardo Sealtiel Martínez Mendoza: Teoría PCF e hipótesis del continuo generalizada revisada

Mexico City Logic Seminar

1/24/2020

Con la teoría de las posibles cofinalidades de Shelah tenemos una herramienta que nos permite estudiar a más profundidad la operación de exponenciación cardinal. Uno de los resultados más destacados que podemos obtener a partir de esta teoría es que si 2^{\aleph_0}<\aleph_{\omega_4}, entonces \aleph_{\omega}^{\aleph_0}<\aleph_{\omega_4}. Otro resultado igual de interesante está relacionado con uno de los problemas centrales de teoría de conjuntos. Sabemos que la hipótesis del continuo generalizada es equivalente a que para cualesquiera cardinales regulares \lambda>\kappa, \lambda^\kappa=\lambda.. Este enunciado se puede aproximar a partir del nivel de cualquier cardinal límite fuerte si consideramos una modificación de la operación de exponenciación cardinal. A esta aproximación se le llama hipótesis del continuo generalizada revisada de Shelah, la cual tiene como consecuencias algunos resultados de carácter combinatorio. Por ejemplo, a partir del primer cardinal límite fuerte, la hipótesis del continuo generalizada es equivalente al principio diamante de Jensen. También, podemos acotar a la celularidad de algunas álgebras booleana con cardinales específicos.

Tagged: Eduardo Sealtiel Martínez Mendoza

Logic Seminar Wed 29 Jan 2020 17:00 hrs at NUS - Talk by Wang Wei

NUS Logic Seminar

1/22/2020

Invitation to the Logic Seminar at the National University of Singapore Date: Wednesday, 29 January 2019, 17:00 hrs Room: S17#04-06, Department of Mathematics, NUS Speaker: Wang Wei, Sun Yat-Sen University, Guangzhou Title: Non-standard models of arithmetic and their standard systems. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: PA is the first order fragment of Peano's axiomatization of the natural numbers. The natural numbers, N, is called the standard model of PA. But by compactness theorem in first order logic, there are also models of PA different from N, which are called non-standard models of arithmetic. Like in N, every element of a non-standard model M has a binary expansion, which can be regarded as the characteristic function of a subset of N. The standard system of M is the collection of all such subsets of N. It is known that standard systems of non-standard models are always Scott sets and every Scott set of cardinality less than or equal to the first uncountable cardinal is the standard system of some non-standard model. However, the general Scott set problem, whether every Scott set is the standard system of some non-standard model, remains one of the major open problems in the model theory of arithmetic. This talk will present some history of Scott set problem, as well as two constructions of non-standard models with uncountable standard systems.

Tagged: Wang Wei

Set Theory Seminar in the Stewart Library this week

Toronto Set Theory Seminar

1/22/2020

Hi everyone,

After some negotiation, we were upgraded to the Stewart Library on the third floor for this week. Here is the info:

Speaker: Henry Yuen

Title: Connes' Embedding Problem through the lens of complexity theory

Location: Fields Institute Stewart Library (#309)

Date and time: Friday, January 24 2020, 1:30-3:00.

Thanks,

Bill

Wednesday seminar

Prague Set Theory Seminar

1/22/2020

Dear all, There is no seminar next week, Wednesday January 29th, there are however still spots to participate the Winter School next week. https://www.winterschool.eu/ The seminars in February are to be decided. No announcement = no seminar. Best, David

(KGRC) research seminar talk on Thursday, January 30

Kurt Godel Research Center

1/22/2020

The KGRC welcomes as guests: Jana Marikova (host: Benjamin Miller) will stay until June 30. Clifton Ealy (host: Benjamin Miller) will visit from March 7 to March 15 and from May 9 to June 30. Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30 and give a talk on January 23. Leandro Aurichi (host: Lyubomyr Zdomskyy) will stay until January 31. Jerzy Kakol (host: Damian Sobota) will stay from March 29 to April 4 and give a talk on April 2. Chi Tat Chong (host: Sy-David Friedman) will stay from June 17 to June 19 and give a talk on June 18. * * * Research seminar Kurt Gödel Research Center Thursday, January 30 "Construction with opposition: Cardinal invariants and games" Víctor Torres-Pérez (TU Wien) We consider several game versions of the cardinal invariants $\mathfrak t$, $\mathfrak u$ and $\mathfrak a$. We show that the standard proof that parametrized diamond principles prove that the cardinal invariants are small actually shows that their game counterparts are small. On the other hand we show that $\mathfrak t < \mathfrak t_{Builder}$ and $\mathfrak u < \mathfrak u_{Builder}$ are both relatively consistent with ZFC, where $\mathfrak t_{Builder}$ and $\mathfrak u_{Builder}$ are the principal game versions of $\mathfrak t$ and $\mathfrak u$, respectively. The corresponding question for $\mathfrak a$ remains open. This is a joint work with Jörg Brendle and Michael Hru\v{s}'ak. Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien

http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Set theory seminar next week: Henry Yuen

Toronto Set Theory Seminar

1/17/2020

Hi everyone,

We will have Henry Yuen of the University of Toronto speaking in the seminar next week. His talk is entitled "Connes' Embedding Problem through the lens of complexity theory"; more details can be found here: http://www.fields.utoronto.ca/talks/Connes-Embedding-Problem-through-lens-complexity-theory

The talk will be held on Friday, January 24 in the Fields Institute from 1:30 to 3:00.

I expect that the seminar will be of broad interest, so please invite your colleagues working in relevant areas to attend. If you will attend the talk, please register using the following link http://www.surveygizmo.com/s3/3247294/Seminar-Registration and send me a reply email indicating your interest, so that I can secure a larger room than our usual meeting place (Fields 210) if needed.

See you there,

Bill Chen

Tagged: Henry Yuen

Set theory seminar tomorrow: Spencer Unger

Toronto Set Theory Seminar

1/16/2020

Hi everyone,

This week Spencer Unger will speak in the seminar. IMPORTANT: note the change in time and place!

The talk will be held on Friday, January 17 in Huron 1018 from 10:00 to 11:00. If you will attend the talk, please register using the following link:

Location: the Huron Building is located on Huron Street adjacent to the Fields Institute and the Bahen Centre. Our room is a seminar room located on the 10th floor. To access this room, please take the elevator to the 9th floor and then walk up one flight of stairs. I will leave from the Fields Institute to the seminar location shortly before the seminar begins.

See you there,

Bill Chen

Tagged: Spencer Unger

Wednesday seminar

Prague Set Theory Seminar

1/14/2020

Dear all, There is no seminar tomorrow Wednesday January 15th. The seminar meets again next week, Wednesday January 22nd at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Egbert Thümmel will speak about omega_1 injective ideals in Boolean algebras, and Jan Šaroch will talk about applications of injective ideals (and set theory in general) in abstract algebra (modules). Best, David

Tagged: Egbert Thümmel

(KGRC) PhD defense and other upcoming talks

Kurt Godel Research Center

1/14/2020

The KGRC welcomes as guests: Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020. Clifton Ealy (host: Benjamin Miller) will stay until January 11, then visit again March 7 to March 15 and May 9 to June 30. Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30, 2020 and give a talk on January 23 (see below). Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19 and give a talk on January 16 (see below). Leandro Aurichi (host: Lyubomyr Zdomskyy) will stay from January 15 to January 31. Jerzy Kąkol (host: Damian Sobota) will stay from March 29 to April 4 and give a talk on April 2. Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020. * * * PhD Defense Kurt Gödel Research Center Wednesday, January 15 "Generalized notions of recurrence: Bases and the existence of invariant probability measures" Jürgen Manuel Inselmann (KGRC) We establish basis and anti-basis theorems for a broad collection of recurrence notions appearing in descriptive, measurable, and topological dynamics, and show that such notions cannot characterize the existence of invariant probability measures in the deacriptive milieu. Time and Place Talk at 10:00am in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien * * * Research seminar Kurt Gödel Research Center Thursday, January 16 "Generalized Cardinal Characteristics for Sets of Functions" Corey Bacal Switzer (City University of New York, Graduate Center, USA) Cardinal characteristics on the generalized Baire and Cantor spaces $\kappa^\kappa$ and $2^\kappa$ have recently generated significant interest. In this talk I will introduce a different generalization of cardinal characteristics, namely to the space of functions $f:\omega^\omega \to \omega^\omega$. Given an ideal $\mathcal I$ on Baire space and a relation $R$ let us define $f R_{\mathcal I} g$ for $f$ and $g$ functions from $\omega^\omega$ to $\omega^\omega$ if and only if $f(x) R g(x)$ for an $\mathcal I$-measure one set of $x \in \omega^\omega$. By letting $\mathcal I$ vary over the null ideal, the meager ideal and the bounded ideal; and $R$ vary over the relations $\leq^*$, $\neq^*$ and $\in^*$ we get 18 new cardinal characteristics by considering the bounding and dominating numbers for these relations. These new cardinals form a diagram of provable implications similar to the Cichoń diagram. They also interact in several surprising ways with the cardinal characteristics on $\omega$. For instance, they can be arbitrarily large in models of CH, yet they can be $\aleph_1$ in models where the continuum is arbitrarily large. They are bigger in the Sacks model than the Cohen model. I will introduce these cardinals, show some of the provable implications and discuss what is known about consistent inequalities, including new generalizations of well-known forcing notions on the reals to this context. This includes joint work with Jörg Brendle. Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien * * * Research seminar Kurt Gödel Research Center Thursday, January 23 "Fake Reflection" Miguel Moreno (Bar-Ilan University, Ramat Gan, Tel Aviv, Israel) Motivated from many results in generalized descriptive set theory, Filter Reflection (aka Fake Reflection) is an abstract version of reflection compatible with large cardinals, forcing axioms, but also V=L. In this talk we will present the motivation and definition of filter reflection, we will explain how to force filter reflection and how to force its failure. We will also show some applications and properties of filter reflection, e.g. the consistency of "$E_{\omega_1}^\kappa$ filter reflects to a subset of $E_{\omega}^\kappa$". Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien

Colloquium this week: Spencer Unger

Toronto Set Theory Seminar

1/13/2020

Hi everyone,

There will be a special colloquium this week given by Spencer Unger of the Hebrew University entitled "A constructive solution to Tarski's circle squaring problem."

The talk will be held in Bahen Centre 6183 on Wednesday, January 15 at 4:00 pm.

https://seminars.math.toronto.edu/seminars/list/events.py/process?start

Stay tuned for updates on Friday's seminar.

Bill

Logic Seminars 15 and 22 January 2020 at NUS

NUS Logic Seminar

1/13/2020

Invitation to the Logic Seminar at the National University of Singapore (1) Date: Wednesday, 15 January 2020, 17:00 hrs Room: S17#04-06, Department of Mathematics, NUS Speaker: Frank Stephan Title: Measure and Conquer for Max Hamming Distance XSAT URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: This talk gives an overview of the joint work of the speaker's recent work on the Hamming XSAT problem. This problem asks for an algorithm to determine which, given an XSAT instance, determines the maximum Hamming distance between two solutions of this instance. The problem has been studied by Dahloef in 2005 in an ISAAC paper who provided an O(1.83848^n) algorithm for this problem. Later Fu, Zhu and Yin presented at JFCST 2012 an O(1.6760^n) algorithm for the related Max Hamming X3SAT problem where all clauses have at most three literals. The current paper provides for the general Max Hamming XSAT problem an O(1.4983^n) algorithm which applies also the technique "Measure and Conquer" in order to prove a better bound than the algorithm would give otherwise. Furthermore, the algorithm does not only provide the maximum Hamming distance of two solutions of the instance, but instead for each k between 0 and n the number of pairs of solutions which have Hamming distance k. For the special case Max Hamming Distant X3SAT, Hoi, Jain and Stephan have the bound O(1.3298^n) at the conference FSTTCS 2019. (2) Date: Wednesday, 22 January 2020, 17:00 hrs Room: S17#04-06, Department of Mathematics, NUS Speaker: Asger Dag Toernquist, Kobenhavns Universitet Title: Mad, med, mcg and other maximal combinatorial objects. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html Abstract: This talk is about the descriptive set theory and infinitary combinatorics. In the past 6 years, a number of long-standing problems related to the definability (in the sense of effective descriptive set theory) of so-called maximal almost disjoint (mad) families, maximal eventually different (med) families, and maximal cofinitary groups (mcg) have been solved by an array of authors. I will give an overview of these developments. Almost disjoint families are families of infinite subsets of omega where any two distinct elements of the family intersect finitely; eventually different families are families of functions from omega to omega such that any two distinct functions in the family are eventually different; and cofinitary groups are subgroups of the group of all permutations of omega with the property that all non-identity elements of the group have at most finitely many fixed points. Maximality of such objects in all cases means maximal under inclusion (among such families). A classical result due to Adrian Mathias states that no analytic infinite mad families. A slew of recent results shed light on this classical result by showing that under suitable descriptive set-theoretic regularity assumptions, there are no mad families at all (and this localizes to suitable pointclasses, especially to analytic sets). In a totally unexpected twist, Horowitz and Shelah showed in 2016 that there are Borel med families and mcg, solving a long-standing problem. I will finish the talk by discussing some related, still unsolved problems, especially the following: Is there a maximal (infinite) analytic set of pairwise Turing-incomparable reals?

Wednesday seminar

Prague Set Theory Seminar

1/3/2020

Dear all, The seminar meets on Wednesday January 8th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. The program is not yet determined, walk-in speakers will be welcome. Best, David

(KGRC) research seminar talk Thursday, January 9

Kurt Godel Research Center

12/30/2019

The KGRC welcomes as guests: Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020. Clifton Ealy (host: Benjamin Miller) will stay until January 11, then visit again March 7 to March 15 and May 9 to June 30. Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30, 2020 and give a talk on January 23. Taras Banakh (host: Lyubomyr Zdomskyy) will stay until January 3. Jaroslav Šupina (host: Vera Fischer) will stay from January 8 to January 10 and give a talk on January 9 (see below). Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19 and give a talk on January 16. Leandro Aurichi (host: Lyubomyr Zdomskyy) will stay from January 15 to January 31. Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020. * * * Research seminar Kurt Gödel Research Center Thursday, January 9 "Ideal pseudointersection numbers and topological spaces" Jaroslav Šupina (Pavol Jozef Šafárik University in Košice, Slovakia) Investigations of ideal versions of selection principles pointed our attention to pseudointersection numbers introduced by P. Borodulin-Nadzieja and B. Farkas 2012 and M. Repický 2018. Both modifications of pseudointersection number are parametrized by ideals on natural numbers and related to orderings among such ideals. We shall focus on these invariants and their connections to selection principles. Their topological characterizations (which resemble Fréchet-Urysohn property) are simple tool to derive inequalities among them. Finally, a result by P. Borodulin-Nadzieja and B. Farkas 2012 shows that ideal version of standard characterization of countable Fréchet-Urysohn property via selection principle by J. Gerlits and Zs. Nagy 1982 is not true. Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien

Maciej Malicki, Continuous Logic VI

IMPAN Working Group in Applications of Set Theory

12/15/2019

Seminar: Working group in applications of set theory, IMPAN Thursday, 19.12.2019, Group lunch (optional): meeting at the reception of IMPAN at 12.30, going elsewhere, "Wiesz co Zjesz" will be closed Seminar at 2:15 pm, room 105, IMPAN, Śniadecki 8, Warsaw. Speaker: Maciej Malicki (Warsaw School of Economics, SGH) Title: "Continuous logic VI" Abstact: "This series of talks will be devoted to a gentle introduction to continuous logic - a natural generalization of first-order logic that is suitable in studying mathematical objects equipped with a metric, e.g. Polish metric spaces and groups, Banach spaces, C*-algebras, etc. Continuous logic is surprisingly parallel to classical logic, and all fundamental concepts such as definable sets, algebraic sets, type spaces, quantifier elimination, omitting types, imaginaries, stability, etc., have their counterparts in this setting. In the final talk, I will define the notion of principal type, and prove the Ryll-Nardzewski theorem for continuous logic. Literature: Ben Yaacov, Itai; Berenstein, Alexander; Henson, C. Ward; Usvyatsov, Alexander; Model theory for metric structures. Model theory with applications to algebra and analysis. Vol. 2, 315--427, London Math. Soc. Lecture Note Ser., 350, Cambridge Univ. Press, Cambridge, 2008.". Visit our seminar webpage which may include announcements of some future talks at https://www.impan.pl/~set_theory/Seminar/ Cheers, Piotr.

(KGRC) research seminar talk Thursday, December 19

Kurt Godel Research Center

12/12/2019

The KGRC welcomes as guests: Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020. Clifton Ealy (host: Benjamin Miller) will stay until January 11, then visit again March 7 to March 15 and May 9 to June 30. Miguel Moreno (host: Lyubomyr Zdomskyy) will stay until November 30, 2020 and give a talk on January 23. Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay until December 22. Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 17 to January 3 and give a talk on December 19 (see below). Jaroslav Supina (host: Vera Fischer) will stay from January 8 to January 10 and give a talk on January 9. Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19 and give a talk on January 16. Leandro Aurichi (host: Lyubomyr Zdomskyy) will stay from January 15 to January 31. Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020. * * * Research seminar Kurt Gödel Research Center Thursday, December 19 "The Golomb space is topologically rigid" Taras Banakh (Ivan Franko National University of Lviv, Ukraine) The Golomb space is the space $\mathcal N$ of natural numbers endowed with the topology generated by the base consisting of arithmetic progressions $a+b\mathbb N$ with coprime parameters $a$ and $b$. The Golomb space is one of the simplest examples of a countable connected Hausdorff space. In this space Topology and Arithmetic are tightly intertwined. We survey topological properties of the Golomb space and prove that this space is topologically rigid, i.e., has trivial homeomorphism group. This resolves a problem posed on Mathoverflow in 2017. Philosophically, the topological rigidity of the Golomb space can be interpreted as the possibility to encode in Topology all Arithmetics (which encodes all Mathematics by the Godel arithmetization). Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien

Wednesday seminar

Prague Set Theory Seminar

12/11/2019

Dear all, The seminar meets on Wednesday December 18th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Jan Grebík -- Hyperfinite equivalence relations Jan will discuss some questions and results concerning hyperfiniteness of Borel equivalence relations both in Borel and measure setting. Let me also remind you that the pre-Christmas meeting of the employees and friends of the Institute of Mathematics CAS does take place on Wednesday after the seminar, at 16:00 in the Institute. Best, David

Set theory seminar this week: Dilip Raghavan

Toronto Set Theory Seminar

12/10/2019

Hi everyone,

This week Dilip Raghavan from the National University of Singapore will speak about Galvin's problem in higher dimensions.

The talk will be held on Friday, December 13 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:

http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Please make note to change the date to December 13 for registration.

See you there,

Bill Chen

Ultrafilters and Ultraproducts Across Mathematics, Pisa, Italy, May 31-June 6, 2020

Conference

12/10/2019

ULTRAMATH 2020 Ultrafilters and Ultraproducts Across Mathematics and Related Topics May 31 - June 6, 2020, Pisa, Italy http://people.dm.unipi.it/ultramath2020/ Dear all, We are happy to announce the upcoming event "ULTRAMATH 2020 - Ultrafilters and Ultraproducts Across Mathematics and Related Topics", that will be held in Pisa (Italy) from May 31st to June 6th 2020. The international Conference "ULTRAMATH 2020” aims to present recent results in the whole spectrum of mathematics which are grounded on the use of ultrafilters and ultraproducts. Its main goals: • Disseminate information about the various techniques related to the use of ultrafilters and ultraproducts, and their potential to attack open problems. • Bring together researchers with different backgrounds, and encourage their collaborations and interactions, especially on topics connecting different areas of mathematics. The covered topics of UltraMath 2020 include (but are not limited to): • Additive and Combinatorial Number Theory. • Combinatorics and Ramsey Theory. • Algebra and Geometry. • General Topology. • Measure Theory. • Ergodic Theory and Dynamics. • Functional Analysis and Metric Spaces. • Nonstandard Analysis and Model Theory. • Generalized Spaces and Differential Equations. • Set Theory. Greater prominence will be given to those results that satisfy (most of) the following conditions: • The results can be formulated and presented in non-specialist terms, and be in principle understandable by any practicing mathematician. • The usage of ultrafilters/ultraproducts is important (or even essential) in obtaining these results. • The results connect different areas of mathematics. • The results reveal new facets of known important topics. This is the second edition of “UltraMath”, after the one held in Pisa in 2008: http://people.dm.unipi.it/ultramath. Scientific Committee: Vitaly Bergelson (Ohio State University, USA) Andreas Blass (University of Michigan, USA) Mauro Di Nasso (Università di Pisa, Italia) Renling Jin (College of Charleston, USA) Organizing Committee: Mauro Di Nasso (Università di Pisa, Italia) – chair Lorenzo Luperi Baglini (Università di Milano, Italia) LIST OF INVITED SPEAKERS Vieri Benci — Università di Pisa, Italia Vitaly Bergelson — Ohio State University, USA Andreas Blass — University of Michigan Ann Arbor, USA Artem Chernikov — University of California Los Angeles (UCLA), USA Natasha Dobrinen — University of Denver, USA Cornelia Druţu — University of Oxford, UK Victoria Gitman — City University of New York (CUNY), USA Isaac Goldbring — University of California Irvine (UCI), USA C. Ward Henson – University of Illinois Urbana-Champaign, USA Neil Hindman — Howard University, USA Michael Hrušák — Universidad Nacional Autónoma, México Renling Jin — College of Charleston, USA Steven Leth — University of Northern Colorado, USA Martino Lupini — Victoria University, New Zealand Joel Moreira — University of Warwick, UK Jaroslav Nešetřil — Charles University Praha, Czech Republic Florian Richter – Northwestern University, USA David A. Ross — University of Hawaii, USA Sławomir Solecki — Cornell University, USA Dona Strauss — University of Hull, UK Simon Thomas — Rutgers University, USA Stevo Todorcevic — Univ. of Toronto, Canada and Univ. Paris Diderot, France There will be a call for contributed papers. Moreover, depending on the funds available, participation of young researchers and researchers from disadvantages areas will be supported. You can preregister by sending an email to ultramath2020@cs.dm.unipi.it with your name and institution. Updated information about UltraMath 2020 will be posted on the website: http://people.dm.unipi.it/ultramath2020/. Those who need more information, can contact the organizers at: ultramath2020@cs.dm.unipi.it. We hope to see you in Pisa! Best regards, The Organizers

http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Tagged: Vieri Benci, Vitaly Bergelson, Andreas Blass, Artem Chernikov, Natasha Dobrinen, Cornelia Druţu, Victoria Gitman, Isaac Goldbring, C. Ward Henson, Neil Hindman, Michael Hrušák, Renling Jin, Steven Leth, Martino Lupini, Joel Moreira, Jaroslav Nešetřil, Florian Richter, David A. Ross, Sławomir Solecki, Dona Strauss, Simon Thomas, Stevo Todorcevic

Logic and Theory Seminar: December 10, 3:00 - 3:50 pm

Boise Logic and Set Theory Seminar

12/9/2019

Colleagues,

The speaker for the final meeting of the Fall 2019 Logic and Set Theory seminar is Dr. Samuel Coskey of the Department of Mathematics. Details are as follows:

Location: Mathematics Building Room 124
Date/time: Tuesday, December 10, 3:00 - 3:50 pm

Title: Locally finite groups and automorphisms

Abstract: The class of finite groups is an amalgamation class, which means that they admit a “Fraisse limit” - a countable structure which contains all the finite groups and which is highly self-symmetric. The limit group is called Hall’s group, it is locally finite, and has the property that any isomorphic finite subgroups are conjugate. In this talk we will give background on Hall’s group and discuss constructing automorphisms of Hall’s group.

Regards,

Marion

Distinguished Professor

Department of Mathematics

Boise State University

Boise, ID 83725

U.S.A.

Tagged: Samuel Coskey

This Week in Logic at CUNY

12/8/2019

This Week in Logic at CUNY:

Hi everyone,

This will be the last regular edition "This Week in Logic at CUNY" until after the winter break (end of January 2020). Special announcements will be sent as necessary in the meantime.

Happy Holidays to all,

Jonas

- - - - Monday, Dec 9, 2019 - - - -

Logic and Metaphysics Workshop
Date: Monday, December 9, 4.15-6.15
Place: Room 7314, CUNY Graduate Center

Mark Colyvan (Sydney)
Title: Logic in Fiction

Abstract: This paper will address the question of whether the logic of a fiction can be specified as part of the fiction. For example, can one tell a fictional story in which it is part of the story that the logic in question is, say, K3? It seems unproblematic that we can do this. After all, we can tell a story about a world with a different geometry from ours, different physical laws, and even different numbers of dimensions (e.g. the two-dimensional world of Flatland). While allowing fictions to specify their own logics seems a natural extension of such science fiction, there are problems looming. Fictions are, by their very nature, incomplete. Specifying that the logic in question is classical is to embrace, amongst other things, classical principles such as excluded middle. But if the fictional world is incomplete, in what sense can it be part of the story that excluded middle holds? We would, in effect, be specifying that the incomplete situation described in the fiction is complete. Imposing excluded middle where it doesn’t belong leads to contradiction. These are especially pressing issues for (particular kinds of) fictionalism about mathematics.

- - - - Tuesday, Dec 10, 2019 - - - -

Computational Logic Seminar
Time 2:00 - 4:00 PM, Room 5382, Tuesday, December 10
Speaker: Sergei Artemov, CUNY Graduate Center
Title: Proving schemes in Peano arithmetic.

Abstract: We will sketch a theory of proving schemes {F(n) | n=0,1,2,…} in Peano arithmetic PA. Obviously, the naïve approach “prove each F(n) in PA” does not work since its justification can easily spill beyond PA. We offer a well-principled definition of a proof of a scheme and establish its basic properties: decidability of proofs, computable enumerability of provable schemes, conservativety of proving schemes (no new theorems), etc. Overall: proving schemes is an intriguing research avenue.

We will then discuss how this theory has influenced our recent proof of PA-consistency. A spoiler: only an explanatory influence, putting the formalized proof of consistency into its rightful place among proofs of schemes in PA.

- - - - Wednesday, Dec 11, 2019 - - - -

- - - - Thursday, Dec 12, 2019 - - - -

- - - - Friday, Dec 13, 2019 - - - -

Friday, December 13, 4:15 PM
Seminar in Logic, Games and Language
CUNY Graduate Center (365 Fifth Avenue, Room 4421)
Glenn Shafer (Rutgers)
Using Game Theory to Reunify Subjective and Objective Probability.

Abstract. Belief and frequency co-existed in the calculus of games of chance as
it was taught in Europe beginning in the 13th century. They still
co-existed in the theory of mathematical probability that Jacob
Bernoulli based on that calculus. But they came apart in the middle of
the 19th century. In this talk, I show how game theory can bring them
back together. My new book with Volodya Vovk (Game-Theoretic
Foundations for Probability and Finance, Wiley, May 2019) bases
mathematical probability on a game with three players: Forecaster (who
offers bets), Skeptic (who decides which offers to take), and Reality
(who decides the outcomes). Forecaster is the Bayesian. Skeptic is the
frequentist. See the working papers at www.probabilityandfinance.com.

Next Week in Logic at CUNY:

- - - - Monday, Dec 16, 2019 - - - -

- - - - Tuesday, Dec 17, 2019 - - - -

- - - - Wednesday, Dec 18, 2019 - - - -

- - - - Thursday, Dec 19, 2019 - - - -

- - - - Friday, Dec 20, 2019 - - - -

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

12/6/2019

Dear all, The seminar meets on Wednesday December 11th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Martin Doležal -- A Turán-type theorem for large-distance graphs in Euclidean spaces Turán’s theorem, a classical result in graph theory, provides an upper bound on the number of edges in any graph with n vertices and with no complete subgraphs on k vertices. We are interested in analogous results for so called large-distance graphs. A large-distance graph is a measurable graph whose vertex set is a measurable subset of Euclidean space, and two vertices are connected by an edge if and only if their distance is larger that 2. We ask for upper bounds on the measures of vertices and edges of a large-distance graph with no complete subgraphs on k vertices. One of our main results says that if A is a measurable subset of a plane such that the large-distance graph of A does not contain any complete subgraph on three vertices then the 2-dimensional Lebesgue measure of A is at most 2π. This is a joint work with J. Hladký, J. Kolář, T. Mitsis, C. Pelekis and V. Vlasák. Best, David

Tagged: Martin Doležal

This Week in Logic at CUNY

12/1/2019

This Week in Logic at CUNY:

- - - - Monday, Dec 2, 2019 - - - -

Logic and Metaphysics Workshop
Date: Monday, December 2, 4.15-6.15
Place: Room 7314, CUNY Graduate Center

Jessica Wilson (Toronto)
Title: On the Notion of Diachronic Emergence

Abstract: Though most accounts of emergence take this to be a broadly synchronic phenomenon, it has been recently maintained that there are distinctively diachronic forms of emergence (see, e.g., O’Connor and Wong’s 2005 account of strong emergence, Mitchell’s 2012 dynamic self-organization account of emergence, and Humphreys’ and Sartenaer and Guay’s 2016 accounts of ‘transformational emergence’). Here I argue that there is no need for a distinctively diachronic notion of emergence, as purported cases of such emergence can either be subsumed under broadly synchronic accounts, or else are better seen as simply cases of causation.

- - - - Tuesday, Dec 3, 2019 - - - -

Computational Logic Seminar
Time 2:00 - 4:00 PM, Room 5382, Tuesday, December 3
Speaker: Sergei Artemov, CUNY Graduate Center
Title: The Provability of Consistency: Interactive Discussion II.

Abstract: We offer a proof of PA-consistency by means of PA. In a nutshell, we view the consistency definition as scheme “S is not a proof of a contradiction in PA” and
i) prove this scheme “given an arbitrary finite sequence of formulas S”;
ii) formalize (i) in PA to secure that no tools outside PA have been used.

We continue with technical details of the proof and its place in the proof theory of PA. As a related thread, we outline the theory of proving arithmetical schemes in PA in a general setting. Our proof is a) contentual consistency proof followed by b) comprehensive formalization of (a) in PA. We discuss why the “standard” approach to proving consistency i) formalization of consistency (either as a formula or a scheme); ii) proving the resulted formalized consistency in PA, is plain wrong at both conceptual and technical levels.

We will then conclude with the promised series of aggregated Q&A's from the previous talks, lectures and discussions.

- - - - Wednesday, Dec 4, 2019 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: Philipp Rothmaler, The Graduate Center and BCC.
Date and Time: Wednesday December 4, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Martsinkovsky-Russell torsion done definably.

Abstract: I will show that the torsion radical in question is, in every module, a (usually infinite) sum of first-order definable subgroups (of the additive group) of the module. Moreover, the collection of formulas involved is uniform: it is all the so-called pp (=positive primitive) formulas that vanish in flat modules. Among the consequences are many of the known features of that torsion theory, as well as new ones. Besides, this lays the foundation for other pp definable torsion radicals, which I will discuss time permitting. Note, the formulas in question constitute functors, namely subfunctors of the forgetful functor.

- - - - Thursday, Dec 5, 2019 - - - -

Computer Science Colloquium
December 5, 2019 (Thursday), 4:15 PM,
CUNY Graduate Center, Room TBA
Yde Venema, ILLC, Universiteit van Amsterdam
Bisimulation invariance: an approach via tree automata

In process theory, at the interface of logic and theoretical computer science, one represents a computational process as a transition system, that is: a collection of states that satisfy certain properties, and are linked by transition relations. For the specification and verification of desired behavior one uses formal logical languages to describe these systems. Since a process can have many distinct representations, one is interested in languages that are expressive enough to express the relevant properties of the process, but not the irrelevant details of its representation. An important notion of equivalence on transition systems is that of a bisimulation: states that are bisimilar (linked by a bisimulation) can be considered to be indistinguishable. As a consequence, properties of states that are not invariant under bisimulations are irrelevant. In this context, it is of interest to identify the bisimulation-invariant fragment of some yardstick logic: If a logic M corresponds to the bisimulation-invariant fragment of a yardstick logic L, then M is strong enough to express all relevant properties of L.

- - - - Friday, Dec 6, 2019 - - - -

Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, December 6, 12:30-2:00pm
Rizos Sklinos, Stevens Institute of Technology
Fields definable in the theory of nonabelian free groups

In this talk I will show that only finite fields are definable in the theory of nonabelian free groups. This is joint work with Ayala Byron.

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, December 6, 2:00-3:30pm
Chris Laskowski, University of Maryland
Counting siblings
Two countable structures are siblings if each is embeddable into the other (e.g., any two countable non-scattered linear orders are siblings). Clearly if M and N are siblings, they have the same finite substructures, hence have the same universal theories. We characterize the universal theories in a finite, relational language that have a countable model with

2 ℵ 0

siblings. This is joint work with Sam Braunfeld.

Next Week in Logic at CUNY:

- - - - Monday, Dec 9, 2019 - - - -

Logic and Metaphysics Workshop
Date: Monday, December 9, 4.15-6.15
Place: Room 7314, CUNY Graduate Center

Kurt Godel Research Center

11/25/2019

The KGRC welcomes as guests: Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020. Clifton Ealy (host: Benjamin Miller) will stay until January 11, then visit again March 7 to March 15 and May 9 to June 30. Istvan Juhasz (host: Sy-David Friedman) will stay from November 25 to December 1 and give a talk on November 28 (see below). Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to November 30, 2020 and give a talk on January 23. Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from December 4 to December 11 and give a talk on December 5 (see below). Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9 to December 22 and give a talk on December 12. Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 17 to January 3 and give a talk on December 19. Jaroslav Supina (host: Vera Fischer) will stay from January 8 to January 10 and give a talk on January 9. Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19 and give a talk on January 16. Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020. * * * Research seminar Kurt Gödel Research Center Thursday, November 28 "Large cardinals in topology" Istvan Juhasz (Renyi Mathematical Institute, Budapest, Hungary) In this talk I intend to deal with a number of problems of general topology that, sometimes rather naturally but sometimes quite surprisingly, lead to or boil down to statements of set theory involving various large cardinals. Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien * * * Research seminar Kurt Gödel Research Center Thursday, December 5 "Specializing trees" Mohammad Golshani (Institute for Research in Fundamental Sciences (IPM), Tehran, Iran) We review our recent work on specializing trees on higher cardinals. The results are based on several joint works with Aspero, Hayut and Shelah. Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien

Set theory seminar this week: Chris Lambie-Hanson

Toronto Set Theory Seminar

11/25/2019

Hello,

This week, Chris Lambie-Hanson from Virginia Commonwealth University will speak in the seminar. The title of his talk is "Set theoretic compactness and higher derived limits."

Abstract: Issues of set theoretic compactness frequently arise when considering questions about derived functors. In particular, the non-vanishing of such derived functors is often witnessed by a concrete combinatorial instance of set theoretic incompactness.

In this talk, we will discuss some recent results about the derived functors of the inverse limit functor. We will focus on a specific inverse system of abelian groups, $\mathbf{A}$ , that arose in Mardešić and Prasolov's work on the additivity of strong homology and has since arisen independently in a number of contexts. Our main result states that, relative to the consistency of a weakly compact cardinal, it is consistent that the $n$ -th derived limits $\lim^n \mathbf{A}$ vanish simultaneously for all $n \geq 1$ . We will sketch a proof of this fact and then discuss the extent to which certain generalizations of this result can hold. This is joint work with Jeffrey Bergfalk.

The talk will be held on Friday, November 29 in Fields 210 from 1:30 to 3:30. If you will attend the talk, please register using the following link:

Please make note to change the date to the date of the seminar (November 29) for registration.

Have a good week,

Bill Chen

This Week in Logic at CUNY

11/24/2019

This Week in Logic at CUNY:

- - - - Monday, Nov 25, 2019 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 11, 4.15-6.15
Place: Room 7314, CUNY Graduate Center

Vincent Alexis Peluce (CUNY)
Title: Memory and Intuitionistic Logic

Abstract: L.E.J. Brouwer writes, “people try by means of sounds and symbols to originate in other people copies of the mathematical constructions and reasonings which they have made themselves; by the same means they try to aid their own memory. In this way the mathematical language comes into being, and as its special case the language of logical reasoning” (1907). More is left to be said, however, about the relation between the Brouwerian subject and logical language. In this talk we discuss the usual account of this relation and some problems with that view. We then propose an alternative.

- - - - Tuesday, Nov 26, 2019 - - - -

Computational Logic Seminar
Time 2:00 - 4:00 PM, Room 5382, Tuesday, November 26
Speaker: Sergei Artemov, CUNY Graduate Center
Title: The Provability of Consistency: Interactive Discussion.

Abstract: Both Hilbert and Gödel objected to viewing Gödel’s Second Incompleteness Theorem as yielding impossibility of proving consistency of a theory by means of the same theory and thus as blocking Hilbert’s consistency program; it was von Neumann who promoted such a reading. Widely popularized, von Neumann’s interpretation is based on two assumptions:
1. Gödel’s consistency formula is the only way to formalize consistency.
2. Any contentual reasoning using principles from T internalizes as a formal derivation in T.
We show that already for Peano arithmetic PA, both of these assumptions are false: (1) does not cover such legitimate mode of presentation as schemes (think of the Induction scheme), (2) fails for schemes. This observation renders von Neumann’s claim unwarranted and supports Hilbert’s and Gödel’s skepticism.

Furthermore, we offer a proof of PA-consistency by means of PA. In a nutshell, we view the consistency definition as scheme “S is not a proof of a contradiction in PA” and
i) prove this scheme “given an arbitrary finite sequence of formulas S”;
ii) formalize (i) in PA to secure that no tools outside PA have been used.

This work has already been widely discussed and we will review the aggregated (long) list of questions and misunderstandings. A teaser: we do not try to derive Gödel’s consistency formula Con(PA) in PA. Moreover, no formal proof in PA can establish mathematical consistency of PA; a successful consistency proof should be contentual.

- - - - Wednesday, Nov 27, 2019 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: James Myer
Date and Time: Wednesday November 27, 2019, 7:00 - 8:30 PM., Room 6417.

Title: Higher-Order Categorical Logic: TBA.

Abstract: We will be starting at 0.6 and go forward.

- - - - Thursday, Nov 28, 2019 - - - -

THANKSGIVING BREAK

- - - - Friday, Nov 29, 2019 - - - -

THANKSGIVING BREAK

Next Week in Logic at CUNY:

- - - - Monday, Dec 2, 2019 - - - -

Logic and Metaphysics Workshop
Date: Monday, December 2, 4.15-6.15
Place: Room 7314, CUNY Graduate Center

Jessica Wilson (Toronto)
Title: On the Notion of Diachronic Emergence

Abstract: Though most accounts of emergence take this to be a broadly synchronic phenomenon, it has been recently maintained that there are distinctively diachronic forms of emergence (see, e.g., O’Connor and Wong’s 2005 account of strong emergence, Mitchell’s 2012 dynamic self-organization account of emergence, and Humphreys’ and Sartenaer and Guay’s 2016 accounts of ‘transformational emergence’). Here I argue that there is no need for a distinctively diachronic notion of emergence, as purported cases of such emergence can either be subsumed under broadly synchronic accounts, or else are better seen as simply cases of causation.

- - - - Tuesday, Dec 3, 2019 - - - -

- - - - Wednesday, Dec 4, 2019 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: Philipp Rothmaler, The Graduate Center and BCC.
Date and Time: Wednesday December 4, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Martsinkovsky-Russell torsion done definably.

Abstract: I will show that the torsion radical in question is, in every module, a (usually infinite) sum of first-order definable subgroups (of the additive group) of the module. Moreover, the collection of formulas involved is uniform: it is all the so-called pp (=positive primitive) formulas that vanish in flat modules. Among the consequences are many of the known features of that torsion theory, as well as new ones. Besides, this lays the foundation for other pp definable torsion radicals, which I will discuss time permitting. Note, the formulas in question constitute functors, namely subfunctors of the forgetful functor.

- - - - Thursday, Dec 5, 2019 - - - -

Computer Science Colloquium
December 5, 2019 (Thursday), 4:15 PM,
CUNY Graduate Center, Room TBA
Yde Venema, ILLC, Universiteit van Amsterdam
Bisimulation invariance: an approach via tree automata

In process theory, at the interface of logic and theoretical computer science, one represents a computational process as a transition system, that is: a collection of states that satisfy certain properties, and are linked by transition relations. For the specification and verification of desired behavior one uses formal logical languages to describe these systems. Since a process can have many distinct representations, one is interested in languages that are expressive enough to express the relevant properties of the process, but not the irrelevant details of its representation. An important notion of equivalence on transition systems is that of a bisimulation: states that are bisimilar (linked by a bisimulation) can be considered to be indistinguishable. As a consequence, properties of states that are not invariant under bisimulations are irrelevant. In this context, it is of interest to identify the bisimulation-invariant fragment of some yardstick logic: If a logic M corresponds to the bisimulation-invariant fragment of a yardstick logic L, then M is strong enough to express all relevant properties of L.

In the talk we introduce the notions of transition systems and bisimulation, and we discuss the bisimulation invariance question for some well-known logics such as first-order and monadic second-order logic. We will mention some recent results that use the notion of alternating tree automata.

This talk is based on joint work with Facundo Carreiro, Alessandro Facchini and Fabio Zanasi.

- - - - Friday, Dec 6, 2019 - - - -

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, December 6, 2:00-3:30pm
Chris Laskowski, University of Maryland
TBA

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

11/20/2019

Dear all, A couple of announcements first: 1) During December 6--9 (Fri--Mon) the Institute of Mathematics will host the 22nd Colloquiumfest. http://users.math.cas.cz/kubis/2019/22colloquiumfest/ Everybody is welcome to attend, there is no conference fee. In order to register, it is enough to send an email to Beata Kubis or Wieslaw Kubis with the relevant data. 2) On Tuesday December 3rd Stevo Todorcevic will deliver the Cech lecture in the Institute. Moreover, Stevo agreed to give a talk at our seminar on Wednesday December 4th. The seminar next week meets on Wednesday November 27th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Jovana Obradović agreed to give us a gentle introduction into her neck of the woods. Title: Combinatorial homotopy theory for operads Abstract: It is a classical result of homotopy theory that algebraic structures with homotopy associative multiplication, such as based loop spaces, admit a nice combinatorial characterization in terms of Stasheff's associahedra. Taking operads as the starting algebraic structure, in this talk we introduce an explicit combinatorial characterization of their strongly homotopy version. In our description, the spaces of operations are defined in terms of hypergraph polytopes, and the composition structure generalizes the one of the Stasheff's associahedra operad. Best, David

UPDATE: This Week in Logic at CUNY

This Week in Logic at CUNY

11/19/2019

Hi everyone,

It's come to my attention that today's talk in the Computational Logic Seminar was erroneously placed under Wednesday, Nov 20 in this week's email. This was human error on my part - the talk was today, Tuesday, Nov 19 (corrected below). My apologies to the speaker and organizers!

Regretfully,

Jonas Reitz

This Week in Logic at CUNY:

- - - - Monday, Nov 18, 2019 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 11, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Matías Bulnes (CUNY)

Title: An Unorthodox Solution to the Hintikka-Kripke Problem

Abstract: The Hintikka-Kripke problem consists in reconciling Hintikka’s semantics for doxastic operators and Kripke’s semantics for alethic operators. The problem arises from their treatment of identity. While the necessity of identities was one of the main innovations of Kripke’s semantics, Hintikka needs identities to be contingent to explain the opacity of doxastic operators. Yet alethic and doxastic operators are combined effortlessly in everyday discourse. In the talk, I will first discuss various attempts at reconciliation within the orthodoxy about opacity, and raise objections to them. Then, I will propose an unorthodox idea: rather than thinking of doxastic operators as introducing new possible worlds with different identities, think of them as introducing new logical spaces with different domains of objects. This achieves reconciliation by circumscribing the necessity of identities to the logical space of each agent. To assess this idea viz-a-viz its competitors, we will have to reexamine some fundamental concepts of the problem of opacity, such as the concepts of language and semantics.

- - - - Tuesday, Nov 19, 2019 - - - -

Computational Logic Seminar
Time 2:00 - 4:00 PM, Room 5382
Tuesday, November 19
Speaker: Sergei Artemov, CUNY Graduate Center
Title: On Logical Foundations of Strategic Games II

Abstract: In his dissertation of 1950, Nash based his concept of the solution to a game on the assumption that “a rational prediction should be unique, that the players should be able to deduce and make use of it”. We study when such definitive solutions exist for strategic games with ordinal payoffs. We show that games without Nash equilibria do not have definitive solutions under any notion of rationality, but each Nash equilibrium can be a definitive solution for an appropriate refinement of Aumann rationality. With respect to Aumann rationality itself, games with multiple Nash equilibria cannot have definitive solutions. Some games with a unique Nash equilibrium have definitive solutions, others don’t, and the criterion for a definitive solution is provided by the iterated deletion of strictly dominated strategies.

- - - - Wednesday, Nov 20, 2019 - - - -

The New York City Category Theory Seminar

Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: Raymond Puzio.
Date and Time: Wednesday November 20, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Posets, Lifting properties, and Completions.

Abstract: Ever since Dedekind, it has been known that special classes of posets can be characterized in terms of forbidden configurations. We note how these characterizations result from lifting properties which, in turn, correspond to propositions in regular logic. This leads us to consider subcategories of morphisms between posets and idempotent completions.

- - - - Thursday, Nov 21, 2019 - - - -

- - - - Friday, Nov 22, 2019 - - - -

Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, November 22, 10:00-11:45am

Brent Cody, Virginia Commonwealth University
A refinement of the Ramsey hierarchy via indescribability

A subset XX of a cardinal κκ is Ramsey if for every function f:[X]<ωo2f:[X]<ωo2 there is a set H⊆XH⊆X of cardinality κκ which is homogeneous for ff, meaning that f↾[H]nf↾[H]n is constant for each n<ωn<ω. Baumgartner proved that if κκ is Ramsey, then the collection of non-Ramsey subsets of κκ is a normal ideal on κκ. We will discuss some recent results concerning Ramsey properties in which homogeneous sets are demanded to be indescribable of a particular degree. Moreover, by iterating Feng's Ramsey operator, which he used to define a notion of αα-Ramseyness of a cardinal κκ, we will consider hypotheses in which homogeneous sets themselves satisfy various Ramsey properties. For ordinals α,β<κα,β<κ we will define a notion of αα-Π1βΠβ1-Ramseyness of a cardinal κκ where αα indicates how many times the Ramsey operator has been iterated and ββ indicates the degree of transfinite indescribability (due to Sharpe-Welch and independently Bagaria) one initially demands homogeneous to satisfy. We will prove that for α,β<κα,β<κ an αα-Π1βΠβ1-Ramsey cardinal is strictly between Feng's αα-Ramsey and an (α+1α+1)-Ramsey cardinal in consistency strength. Moreover, for fixed α<κα<κ, as ββ increases the αα-Π1βΠβ1-Ramsey cardinals yield a strictly increasing hierarchy, in a somewhat subtle sense. For β0<β1<κβ0<β1<κ and for large enough α<κα<κ, κκ being αα-Π1β0Πβ01-Ramsey is equivalent to κκ being αα-Π1β1Πβ11-Ramsey (we will identify the least αα at which this equivalence occurs). But if α,β0<κα,β0<κ there is a large enough β1<κβ1<κ such that κκ being αα-Π1β0Πβ01-Ramsey is strictly weaker than κκ being αα-Π1β1Πβ11-Ramsey. All of these results seem to require a careful analysis of the ideals associated to the various large cardinal notions.

Model Theory Seminar

CUNY Graduate Center, Room 6417

Friday, November 22, 12:30-2:00pm

Alex Kruckman, Wesleyan University
A diversity of Kim's Lemmas

One of the most important steps in the development of simplicity theory by Kim and Pillay in the 1990s was a result now known as Kim's Lemma: In a simple theory, if a formula divides, then this dividing is witnessed by every Morley sequence in the appropriate type. More recently, variants on Kim's Lemma have been shown (by Chernikov, Kaplan, and Ramsey) to follow from, and in fact characterize, the combinatorial dividing lines NTP2 and NSOP1: two generalizations of simplicity in different directions. After surveying the Kim's Lemmas of the past, I will speculate about a new combinatorial dividing line, generalizing both NTP2 and NSOP1 and characterized by a new variant of Kim's Lemma. This is joint speculation with Nick Ramsey.

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, November 22, 2:00-3:30pm

Alex Kruckman, Wesleyan University
Interpolative fusions

Fix languages L and L' (possibly non-disjoint). An structure M in the union of these languages is interpolative if whenever X is an L-definable set in M and X' is an L'-definable set in M, X and X' intersect unless they are separated by disjoint definable sets in the intersection of L and L'. When T is an L theory and T' is an L' theory, we say that a theory T* is the interpolative fusion of T and T' if it axiomatizes the class of interpolative models of the union of T and T'. If T and T' are model-complete, this is exactly the model companion of the union theory. Interpolative fusions provide a unified framework for studying many examples of 'generic constructions' in model theory. Some, like structures with generic predicates, or algebraically closed fields with several independent valuations, are explicitly interpolative fusions, while others, like structures with generic automorphisms, or fields with generic operators, are bi-interpretable with interpolative fusions. In joint work with Erik Walsberg and Minh Tran, we study two basic questions: (1) When does the interpolative fusion exist, and how can we axiomatize it? (2) How can we understand properties of the interpolative fusion T* in terms of properties of the theories T, T', and their intersection?

Next Week in Logic at CUNY:

- - - - Monday, Nov 25, 2019 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 11, 4.15-6.15
Place: Room 7314, CUNY Graduate Center

Vincent Alexis Peluce (CUNY)
Title: Memory and Intuitionistic Logic

Abstract: L.E.J. Brouwer writes, “people try by means of sounds and symbols to originate in other people copies of the mathematical constructions and reasonings which they have made themselves; by the same means they try to aid their own memory. In this way the mathematical language comes into being, and as its special case the language of logical reasoning” (1907). More is left to be said, however, about the relation between the Brouwerian subject and logical language. In this talk we discuss the usual account of this relation and some problems with that view. We then propose an alternative.

- - - - Tuesday, Nov 26, 2019 - - - -

- - - - Wednesday, Nov 27, 2019 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: James Myer
Date and Time: Wednesday November 27, 2019, 7:00 - 8:30 PM., Room 6417.

Title: Higher-Order Categorical Logic: TBA.

Abstract: We will be starting at 0.6 and go forward.

- - - - Thursday, Nov 28, 2019 - - - -

THANKSGIVING BREAK

- - - - Friday, Nov 29, 2019 - - - -

THANKSGIVING BREAK

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io [nylogic.github.io]
(site designed, built & maintained by Victoria Gitman)

Set theory seminar this week: Vinicius Rodrigues

Toronto Set Theory Seminar

11/19/2019

Hi everyone,

This week, Vinicius Rodrigues of the University of São Paulo will speak in the seminar. His talk is entitled "Psi spaces with pseudocompact hyperspaces."

Abstract: The Hyperspace of Vietoris of a topological space X is a topology given to the space of nonempty closed subsets of X. A famous theorem due to Vietoris states that X is compact iff its hyperspace is compact, so the natural question of whether there are other relations between the two spaces with respect to notions that generalize compactness arise. J. Ginsburg has asked whether for a space X, X^omega pseudocompact implies that the hyperspace of X is pseudocompact. A negative answer was given by M. Hrusak, I. Martinez-Ruiz, and F. Hernandez-Hernandez. They also studied this question restricted to psi spaces of MAD families, and, restricted to these psi spaces, the answer is independent of ZFC. However, it is not known if, in ZFC, there exists a MAD family whose psi space has pseudocompact hyperspace. V. Rodrigues and A. Tomita showed that it is consistent that there exists two MAD families, one whose psi space has pseudocompact hyperspace, and one whose psi space hasn't.

The talk will be held on Friday, November 22 in Fields 210 from 1:30 to 3:30. If you will attend the talk, please register using the following link:

http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Please make note to change the date to the date of the seminar (November 22) for registration.

Thanks!

Bill

(KGRC) upcoming talks in the research seminar

Kurt Godel Research Center

11/18/2019

The KGRC welcomes as guests: Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020. Clifton Ealy (host: Benjamin Miller) will stay until January 11, then visit again March 7 to March 15 and May 9 to June 30. Sarka Stejskalova (host: Sy-David Friedman) will stay from November 21 to November 22. Radek Honzik (host: Sy-David Friedman) will stay from November 21 to November 22. Istvan Juhasz (host: Sy-David Friedman) will stay from November 25 to December 1 and give a talk on November 28 (see below). Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to November 30, 2020 and give a talk on January 23. Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from December 4 to December 11 and give a talk on December 5. Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9 to December 22 and give a talk on December 12. Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 17 to January 3 and give a talk (talk to be confirmed). Jaroslav Supina (host: Vera Fischer) will stay from January 8 to January 10 and give a talk on January 9. Corey Switzer (host: Vera Fischer) will stay from January 12 to January 19 and give a talk on January 16. Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020. * * * Research seminar Kurt Gödel Research Center Thursday, November 21 "Cichon's Maximum without large cardinals" Martin Goldstern (TU Wien) How many Lebesgue null sets are needed to cover the real line? How many functions (from the natural numbers to the natural numbers) are needed to dominate all functions? The answers to these questions and 10 more related questions are certain uncountable cardinals collected in Cichon's Diagram, which also shows provable inequalities between these cardinals. In a recent joint work with Jakob Kellner, Diego Mejia and Saharon Shelah, we constructed a model where the cardinals in Cichon's Diagram have 10 different values (which is known to be best possible). The construction first uses a finite support iteration P to get 5 different values for the left side of the diagram, and then finds a subset P' which also separates the values on the right side. Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien * * * Research seminar Kurt Gödel Research Center Thursday, November 28 "Large cardinals in topology" Istvan Juhasz (Renyi Mathematical Institute, Budapest, Hungary) In this talk I intend to deal with a number of problems of general topology that, sometimes rather naturally but sometimes quite surprisingly, lead to or boil down to statements of set theory involving various large cardinals. Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien

Tagged: Martin Goldstern, István Juhász

Logic and Set Theory Seminar: November 19, 3:00 - 3:50 pm

Boise Logic and Set Theory Seminar

11/18/2019

Colleagues,

The speaker for the next meeting of the Fall 2019 Logic and Set Theory seminar is Dr. Randall Holmes of the Department of Mathematics. Details are as follows:

Location: Mathematics Building Room 124
Date/time: Tuesday, November 19, 3:00 - 3:50 pm

Title: The axiom of cantorian sets in NFU and the existence of n-Mahlo cardinals - PART 2

Abstract: We report on some observations of Robert Solovay, somewhat extended and refined by the speaker, regarding the relationship between the seemingly innocent Axiom of Cantorian Sets proposed by C Ward Henson for NF a long time ago, and the existence of n-Mahlo cardinals. A partition theorem of Schmerl will be described which handles the relationship in one direction.

Regards,

Marion Scheepers

Distinguished Professor

Department of Mathematics

Boise State University

Boise, ID 83725

U.S.A.

This Week in Logic at CUNY

11/17/2019

This Week in Logic at CUNY:

- - - - Monday, Nov 18, 2019 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 11, 4.15-6.15
Place: Room 7314, CUNY Graduate Center
Matías Bulnes (CUNY)

Title: An Unorthodox Solution to the Hintikka-Kripke Problem

Abstract: The Hintikka-Kripke problem consists in reconciling Hintikka’s semantics for doxastic operators and Kripke’s semantics for alethic operators. The problem arises from their treatment of identity. While the necessity of identities was one of the main innovations of Kripke’s semantics, Hintikka needs identities to be contingent to explain the opacity of doxastic operators. Yet alethic and doxastic operators are combined effortlessly in everyday discourse. In the talk, I will first discuss various attempts at reconciliation within the orthodoxy about opacity, and raise objections to them. Then, I will propose an unorthodox idea: rather than thinking of doxastic operators as introducing new possible worlds with different identities, think of them as introducing new logical spaces with different domains of objects. This achieves reconciliation by circumscribing the necessity of identities to the logical space of each agent. To assess this idea viz-a-viz its competitors, we will have to reexamine some fundamental concepts of the problem of opacity, such as the concepts of language and semantics.

- - - - Tuesday, Nov 19, 2019 - - - -

- - - - Wednesday, Nov 20, 2019 - - - -

Computational Logic Seminar
Time 2:00 - 4:00 PM, Room 5382
Tuesday, November 19
Speaker: Sergei Artemov, CUNY Graduate Center
Title: On Logical Foundations of Strategic Games II

Abstract: In his dissertation of 1950, Nash based his concept of the solution to a game on the assumption that “a rational prediction should be unique, that the players should be able to deduce and make use of it”. We study when such definitive solutions exist for strategic games with ordinal payoffs. We show that games without Nash equilibria do not have definitive solutions under any notion of rationality, but each Nash equilibrium can be a definitive solution for an appropriate refinement of Aumann rationality. With respect to Aumann rationality itself, games with multiple Nash equilibria cannot have definitive solutions. Some games with a unique Nash equilibrium have definitive solutions, others don’t, and the criterion for a definitive solution is provided by the iterated deletion of strictly dominated strategies.

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: Raymond Puzio.
Date and Time: Wednesday November 20, 2019, 7:00 - 8:30 PM., Room 6417.
Title: Posets, Lifting properties, and Completions.

Abstract: Ever since Dedekind, it has been known that special classes of posets can be characterized in terms of forbidden configurations. We note how these characterizations result from lifting properties which, in turn, correspond to propositions in regular logic. This leads us to consider subcategories of morphisms between posets and idempotent completions.

- - - - Thursday, Nov 21, 2019 - - - -

- - - - Friday, Nov 22, 2019 - - - -

Set Theory Seminar
CUNY Graduate Center, Room 6417
Friday, November 22, 10:00-11:45am

Brent Cody, Virginia Commonwealth University
A refinement of the Ramsey hierarchy via indescribability

A subset XX of a cardinal κκ is Ramsey if for every function f:[X]<ωo2f:[X]<ωo2 there is a set H⊆XH⊆X of cardinality κκ which is homogeneous for ff, meaning that f↾[H]nf↾[H]n is constant for each n<ωn<ω. Baumgartner proved that if κκ is Ramsey, then the collection of non-Ramsey subsets of κκ is a normal ideal on κκ. We will discuss some recent results concerning Ramsey properties in which homogeneous sets are demanded to be indescribable of a particular degree. Moreover, by iterating Feng's Ramsey operator, which he used to define a notion of αα-Ramseyness of a cardinal κκ, we will consider hypotheses in which homogeneous sets themselves satisfy various Ramsey properties. For ordinals α,β<κα,β<κ we will define a notion of αα-Π1βΠβ1-Ramseyness of a cardinal κκ where αα indicates how many times the Ramsey operator has been iterated and ββ indicates the degree of transfinite indescribability (due to Sharpe-Welch and independently Bagaria) one initially demands homogeneous to satisfy. We will prove that for α,β<κα,β<κ an αα-Π1βΠβ1-Ramsey cardinal is strictly between Feng's αα-Ramsey and an (α+1α+1)-Ramsey cardinal in consistency strength. Moreover, for fixed α<κα<κ, as ββ increases the αα-Π1βΠβ1-Ramsey cardinals yield a strictly increasing hierarchy, in a somewhat subtle sense. For β0<β1<κβ0<β1<κ and for large enough α<κα<κ, κκ being αα-Π1β0Πβ01-Ramsey is equivalent to κκ being αα-Π1β1Πβ11-Ramsey (we will identify the least αα at which this equivalence occurs). But if α,β0<κα,β0<κ there is a large enough β1<κβ1<κ such that κκ being αα-Π1β0Πβ01-Ramsey is strictly weaker than κκ being αα-Π1β1Πβ11-Ramsey. All of these results seem to require a careful analysis of the ideals associated to the various large cardinal notions.

Model Theory Seminar

CUNY Graduate Center, Room 6417

Friday, November 22, 12:30-2:00pm

Alex Kruckman, Wesleyan University
A diversity of Kim's Lemmas

One of the most important steps in the development of simplicity theory by Kim and Pillay in the 1990s was a result now known as Kim's Lemma: In a simple theory, if a formula divides, then this dividing is witnessed by every Morley sequence in the appropriate type. More recently, variants on Kim's Lemma have been shown (by Chernikov, Kaplan, and Ramsey) to follow from, and in fact characterize, the combinatorial dividing lines NTP2 and NSOP1: two generalizations of simplicity in different directions. After surveying the Kim's Lemmas of the past, I will speculate about a new combinatorial dividing line, generalizing both NTP2 and NSOP1 and characterized by a new variant of Kim's Lemma. This is joint speculation with Nick Ramsey.

Logic Workshop
CUNY Graduate Center, Room 6417
Friday, November 22, 2:00-3:30pm

Alex Kruckman, Wesleyan University
Interpolative fusions

Fix languages L and L' (possibly non-disjoint). An structure M in the union of these languages is interpolative if whenever X is an L-definable set in M and X' is an L'-definable set in M, X and X' intersect unless they are separated by disjoint definable sets in the intersection of L and L'. When T is an L theory and T' is an L' theory, we say that a theory T* is the interpolative fusion of T and T' if it axiomatizes the class of interpolative models of the union of T and T'. If T and T' are model-complete, this is exactly the model companion of the union theory. Interpolative fusions provide a unified framework for studying many examples of 'generic constructions' in model theory. Some, like structures with generic predicates, or algebraically closed fields with several independent valuations, are explicitly interpolative fusions, while others, like structures with generic automorphisms, or fields with generic operators, are bi-interpretable with interpolative fusions. In joint work with Erik Walsberg and Minh Tran, we study two basic questions: (1) When does the interpolative fusion exist, and how can we axiomatize it? (2) How can we understand properties of the interpolative fusion T* in terms of properties of the theories T, T', and their intersection?

Next Week in Logic at CUNY:

- - - - Monday, Nov 25, 2019 - - - -

Logic and Metaphysics Workshop
Date: Monday, November 11, 4.15-6.15
Place: Room 7314, CUNY Graduate Center

Vincent Alexis Peluce (CUNY)
Title: Memory and Intuitionistic Logic

Abstract: L.E.J. Brouwer writes, “people try by means of sounds and symbols to originate in other people copies of the mathematical constructions and reasonings which they have made themselves; by the same means they try to aid their own memory. In this way the mathematical language comes into being, and as its special case the language of logical reasoning” (1907). More is left to be said, however, about the relation between the Brouwerian subject and logical language. In this talk we discuss the usual account of this relation and some problems with that view. We then propose an alternative.

- - - - Tuesday, Nov 26, 2019 - - - -

- - - - Wednesday, Nov 27, 2019 - - - -

The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York

Speaker: TBA
Date and Time: Wednesday November 27, 2019, 7:00 - 8:30 PM., Room 6417.

Title: Higher-Order Categorical Logic: TBA.

Abstract: We will be starting at TBA and go forward.

- - - - Thursday, Nov 28, 2019 - - - -

THANKSGIVING BREAK

- - - - Friday, Nov 29, 2019 - - - -

THANKSGIVING BREAK

- - - - Other Logic News - - - -

- - - - Web Site - - - -

Find us on the web at: nylogic.github.io [nylogic.github.io]
(site designed, built & maintained by Victoria Gitman)

-------- ADMINISTRIVIA --------

To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.

If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.

Wednesday seminar

Prague Set Theory Seminar

11/14/2019

PS: I just noticed this announcement: http://www.math.cas.cz/documents/cech16.pdf Stevo Todorcevic will deliver a distinguished lecture on Tuesday December 3rd 2019 at 10:30 in the Institute of Mathematics CAS. Best, David On 14/11/2019 09:50, David Chodounsky wrote: > Dear all, > > The seminar meets on Wednesday November 20th at 11:00 in the Institute > of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. > > Program: Osvaldo Guzman -- The splitting and the ultrafilter numbers > > Blass and Shelah showed that it is consistent that the ultrafilter > number is smaller than the splitting number. In this talk, we will > provide a different proof that this inequality is consistent. This is a > part of a joint work with Damjan Kalajdzievski. > > > > Best, > David

Wednesday seminar

Prague Set Theory Seminar

11/14/2019

Dear all, The seminar meets on Wednesday November 20th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building. Program: Osvaldo Guzman -- The splitting and the ultrafilter numbers Blass and Shelah showed that it is consistent that the ultrafilter number is smaller than the splitting number. In this talk, we will provide a different proof that this inequality is consistent. This is a part of a joint work with Damjan Kalajdzievski. Best, David

Set theory seminar this Friday

Toronto Set Theory Seminar

11/12/2019

Hi everyone,

We will have Jan Pachl speaking in the seminar this week about DTC ultrafilters on groups.

Abstract: An infinite finitely generated group G is virtually abelian if and
only if it does not admit a DTC ultrafilter = an ultrafilter that
determines the topological centre of the semigroup βG.
More generally, we have necessary conditions and, for countable groups,
sufficient conditions for the existence of DTC ultrafilters.
This is joint work with Juris Steprans.

The talk will be held on Friday, November 15 in Fields 210 from 1:30 to 3:30. If you will attend the talk, please register using the following link:

http://www.surveygizmo.com/s3/3247294/Seminar-Registration

Please make note to change the date to the date of the seminar (November 15) for registration.

Thanks!

Bill Chen

Fwd: Set Theory Seminar this week

Toronto Set Theory Seminar

11/12/2019

Hi everyone,

This Friday, Juris will continue with the second part of his talk.

The talk will be held on Friday November 8 at Fields 210 from 1:30 to 3:00, as usual. If you will attend the talk, please register using the following link:
http://www.surveygizmo.com/s3/3247294/Seminar-Registration

See you there,

Bill Chen

Fwd: Set theory seminar

Toronto Set Theory Seminar

11/12/2019

Place: Fields Institute (Room 210) Date: November 1, 2019 (13:30-15:00) Speaker: Juris Steprans Title: A model where $\mathfrak s = \mathfrak b < \mathfrak a$

(KGRC) talk in the research seminar Thursday, November 14

Kurt Godel Research Center

11/11/2019

The KGRC welcomes as guests: Jana Marikova (host: Benjamin Miller) will stay until June 30, 2020. Clifton Ealy (host: Benjamin Miller) will stay until January 11, 2020, then visit again March 7 to March 15 and May 9 to June 30. Sarka Stejskalova (host: Sy-David Friedman) will stay from November 21 to November 22. Radek Honzik (host: Sy-David Friedman) will stay from November 21 to November 22. Istvan Juhasz (host: Sy-David Friedman) will stay from November 25 to December 1 and give a talk on November 28. Miguel Moreno (host: Lyubomyr Zdomskyy) will stay from December 1, 2019 to November 30, 2020 and give a talk on January 23. Mohammad Golshani (hosts: Sy-David Friedman, Yair Hayut) will stay from December 4 to December 11 and give a talk on December 5. Oleksandr Ravsky (host: Lyubomyr Zdomskyy) will stay from December 9 to December 22 and give a talk on December 12. Taras Banakh (host: Lyubomyr Zdomskyy) will stay from December 17, 2019 to January 3, 2020 and give a talk (talk to be confirmed). Jaroslav Supina (host: Vera Fischer) will give a talk on January 9, 2020. Corey Switzer (host: Vera Fischer) will stay from January 12, 2020 to January 19, 2020 and give a talk on January 16. Chi Tat Chong (host: Sy-David Friedman) will give a talk on June 18, 2020. * * * Research seminar Kurt Gödel Research Center Thursday, November 14 "L[Reg]" Sy-David Friedman (KGRC) Gitik and I showed that L[Reg], like L[Card] and V, is a forcing extension of an iterate of a mouse. For L[Card] the mouse is the least one with a measurable limit of measurables (result of Philip Welch) and for V it's Mighty Mouse. For L[Reg] it's the least mouse with a measure concentrating on measurables, but the iterate may have to be truncated (for example if there are no regular limit cardinals). We use Magidor's iteration of Prikry forcings. An unexpected twist is that we need to use old-fashioned mice and not fine-structural mice for the proof. Time and Place Tea at 3:30pm in the KGRC meeting room (seminar room CST5.47) Talk at 4:00pm in the KGRC lecture room (seminar room D5.48) Universität Wien Institut für Mathematik Kurt Gödel Research Center Augasse 2-6, UZA 1 - Building 2 1090 Wien